Okay. Good morning everyone. Good morning to those online as well. Let's just pray and we'll begin. Father we thank you again for this wonderful day God. We thank you for giving us yet another opportunity to come and learn and Lord we just come in this day into your hands, we come in our hearts, our spirit of God and Lord even as we will just receive from you, pray God that everything that we learn will be fruitful in our lives a God that we will see a change, we will see our lives being transformed to God. We thank you for what you have done thus far and what you're going to do in each of our lives. In Jesus' name we pray. Amen. Amen. Okay. So last class we did up to chapter 91 and I was going through the notes. So from chapter 92, this is section 10, a lot of the chapters are repeated, right? So there will be a couple of chapters I just may move on but what I want to do is I want to complete as much as I can this this class and then we'll close for this course, right? So whatever's remaining most of it is repeated so you can just go back and read it but I want to finish the course just this session and then I will post the assessments on the Google classroom as well, right? So let's just continue from chapter 92 and I may skip a few chapters just to help us to cover as much as we can, okay? So we talked about an inheritance, right? We talked about God that he has given us an inheritance when we believe in Christ and he has qualified us to be part of that inheritance. Everybody know what inheritance is, no? Yes, right? Something of the parents goes to the children automatically. They don't deserve it, they don't earn it but it's an inheritance, right? Efficiency 1, 3, we talked about blessed with every spiritual blessing, every blessing that is there in Jesus Christ is available for you and I as believers, right? Efficiency 1, 3. James 1, 17 says every good gift and every perfect gift is from above and comes down from the Father of lights with whom there is no variation or shadow of turning. So we are blessed with every blessing. Then chapter 96 we talked about being enriched by Him meaning, remember the Lord Jesus, what did He say? I am the vine, you are the branches. If you are not connected, if you're connected to me, you will bear fruit. If you are not connected, you will not bear fruit, yes? Right? So imagine a vine tree, if you're not connected to the main stem, you will not bear fruit. If you look at it, any plant, right? If you're not connected to the stem, you will not bear fruit. So here, when we talk about enriched in Christ, meaning everything that we have flows out from Him, right? So when we have gifts and talents and the gifts of the Holy Spirit working in our lives, it is through whom? Through? Through the Lord Jesus, right? Nothing is of our own, right? So it says here, 1 Corinthians 1 and verse 5, that you were enriched in everything by Him. He has enriched you. Now it is our choice to continue to be connected or not connected. That's our choice, right?  You will understand your potential that God has given you. Chapter 97, again, we are always triumphant. Many of us, people ask me this question, right? When the Bible says we are always triumphant, meaning we are always victorious, but why is it in life as believers, we see so many failures, we see so many challenges, right? Now the answer is, we are living a life in a world where the enemy is working, right? So we will fail. There will be times we will, you know, we will fall. There will be times we will feel weak and weary, but we are triumphant in Christ when we put our trust in Him. So even in our failures, when we say Lord Jesus, I thank you for who you are. I thank you that even this season, you are faithful. Who's victorious? In the natural, it looks like a failure, but for God, it is a victory. Best example is the cross, right? When you look at the cross, what is it? Does it look like victory or does it look like failure? What does it look like? Failure or victory? It says here that in... Victory pastor. In Christ. Thank you, Gertrude. In Christ, we are what? triumphant. They are victorious. So the devil will come and say, hey, hey, we're a failure. What should you say? Yes. What will you say? Because in that situation, in that season, it may look like a failure, but you're not a failure. You're not. Like even as leaders, as, you know, being pastoring church in the church, there are many times we feel like a failure. But remember that ministry and Christianity is not about how we feel. It's not a feeling. I can feel weak. I can feel happy. I can feel anointed, but it's not a feeling. It is faith. Right? It's not only emotions. It is faith. We have to believe it. Are you understanding what I'm saying? Right? So they're always triumphant. And then in 1st Timothy 612, Paul is saying, you fight the good fight of faith.  In 1st, 2nd Corinthians, Paul is saying, you are triumphant in Christ. You're already victorious. But in 1st Timothy, Paul is saying, you fight the good fight. And we can ask Paul to know. You said we are already victorious. Why are you saying fight the good fight? That means what? Every day of our life, we are to walk in that victorious life. Will there be failures? Yes. As leaders, as pastors, have we faced failures many times. But we stand up again. We say, God, you are with me. Help me to be victorious. Help me to walk in that identity. Right? And that is something that we have to do. Then we are born to overcome. And when we talk about overcome, it means not only in the spiritual, but overcome in our mind, overcome in our body, overcome the situations, every area of our life we are called to overcome. Right? Now, imagine this. You're in ministry. Okay? And you're doing ministry. Your church is growing. Your ministry is growing. But you're not able to overcome certain thoughts in your mind. Right? Nobody knows. When people look at you, they'll say, Jai Masi Ki. Where's the Lord Pastor Ji? But in your mind, there is still, in the mind, there are still areas where the devil is still working strongly. They've not overcome. That means what? We have allowed the devil to work in our mind and we are not living this overcoming life. But outside, it looks like we are strong. Remember, I mentioned this, God will work even though whether we pray or not pray, God works. Yes or no? Right? In spite of us, he will work. Right? But we are called to overcome in all areas of our life. Say, all areas. Not one area. Not just one area. We must be able to overcome in our mind, in our thoughts, in our words. You know, I've met people and these are well meaning believers. They come up to me and say, I don't know why, but when I open my mouth, I speak lies. It's not required. Are we talking normally? Suddenly, I'll say something. It's a lie. I don't know why. It's not required. It was not needed. But it's... What can you tell them? He said, we must have control. We must overcome the words that we speak. We must be wise in the words that we speak. That, again, is an ability that we must develop. Right? Sometimes, it's not only about talking. It's about just keeping quiet. Yes or no? Yes? Okay. Then we have the promise of life. We are sealed with the Spirit. Okay, I want to stay on this chapter 100. Sealed in the Spirit. Okay, let's read Ephesians 1 13 and 14. In him you also trusted, after you heard the word of truth, the gospel of your salvation and whom also, having believed, you were sealed with the Holy Spirit of promise, who is the guarantee of our inheritance until the redemption of the purchase possession to the praise of his glory. Okay, everyone say this, sealed with the Spirit. Now, you know, when you imagine, I give you a document, right? A Bible College document. I say, this is your Mark's card. Example, right? Now, if it's just a paper with your marks, is it holding any value? Why? The seal is not there. Right? So you know the importance of a seal. Imagine I write one letter and I, you know, I just, I just say this is Paul Emanuel. It's not going to have any authority. But the moment there's a seal on it, that seal will signify that you belong to this organization. Right?  So sealing means you belong to somebody. In the olden days, what they would do is when farmers had cattle, right? They had sheep and goats and, you know, cows and all of those cattle, herding cattle, they had so much that they used to seal the animals also. They used to brand them. Right? So for example, they'll put a initial on the animal, their market. So wherever the animal goes, see the seal, this is mine. Right? It was also to identify some that you belong to somebody. Now Paul is saying here, you are sealed with what? The Holy Spirit. Now imagine you take a seal, you stamp it on the paper. Is it easy to rub it off? Can it take, you know, you get these rubbers, erasers, you know, can you do it? Even if you do it, it's not clear. You can make out somebody has tampered with this. So think of it this way. The Lord Jesus has sealed you with the Holy Spirit. Right? He has, so this is you. He has sealed you with the Holy Spirit. Now what the enemy is trying is, he's going, he's trying to rub out that seal. No. There's no seal on the paper. It's still like before in the day. What does it say here? He has sealed you with the promise of the Holy Spirit. So you've been sealed. Where is my seal on my body? It's not a physical seal. It is a spiritual seal. It's a seal that God knows and you know that it's there inside you. Even? Right? And this is such a powerful, powerful aspect to know that we have the seal of the Holy Spirit. So when the devil comes, you can just open your heart and say, here's my seal. Here's my seal, the promise of the Holy Spirit. The devil will say, no, but you did all these failures, all these sins. This is all the wrong things that you did. He said, okay, I will go ask God for forgiveness. But this is the seal of the Holy Spirit. He's still there. Maybe I'm not using it, but he's there. What does Paul say? Do not grieve the Holy Spirit. Now, think of this. We become believers. The Holy Spirit has come and he's living inside us. When we sin, does the Holy Spirit go away? When we keep sinning, does the Holy Spirit go away? No. But what have we done? We have silenced or we have suppressed or we have grieved the Holy Spirit. We have made him sad. So he's there, but he's not working in our life because we are allowing other things in our life to take priority. But the seal is still there. Imagine this. It's like somebody comes and asks you, hey, what did you do for three years in Bangalore? I was in Bangalore. What were you doing? I joined Bible college and I graduated from Bible college. Oh, good, very good. So why don't you do something else in terms of, in Bible college? But why don't you join as a teacher? This is an example, right? Why don't you join as a teacher? It says, oh, no, let me. I don't know if I have the documents. I don't know if I have the ability to do that. Now, you have the ability. You have the certificate with the stamp, but we're not showing it. And this person is saying, you have proof that you are studied for three years? So yeah, I have proof. Where's the proof? It's there. Bring it to me. No, no need that. It's not required. And does it make sense? Because it's the same way. You're sealed with the Holy Spirit. The devil tries to tell you there is nothing you can do. There is no Holy Spirit. The Holy Spirit is not working in your life. You cannot prophesy. You cannot have word of knowledge. Why? Because you are just a believer. That's all you are. You cannot be a pastor. You cannot be a prophet. You cannot write songs. You cannot come up with your own songs. All of this is the work of the devil. But what should you do? Say, devil, I am sealed by the Holy Spirit. Nobody can take out that seal. Even God won't take out that seal. It's there. Now, whether we use the paper with the seal, whether we use it or not, it is our choice. Everyone understood this. So we are preserved in Christ, meaning the word preserved means to take care of, to guard, to keep it in good condition. So for example, I say, Joseph, I'm giving you this laptop. I'm going to come back after one year and I'll take it back from you after one year. But for one year, you can use the laptop. I don't need it for one year. Now, what is Joseph going to do? He has two choices. Like always, there can be all kinds of food on this laptop, very dirty, broken, or he can preserve it and say, hey, one year, let me wipe it. Let me make sure I look after it well, so that when I give it back, it will be in a better condition than I got it. That is called preserve. Right? We are preserved in Christ.  This is my son. This is my daughter. I preserve them. They are valuable to me. So we are preserved from the works of the devil. We are preserved from the enemy. God preserves us from the things of the flesh. He keeps us away from it. Again, the choice is ours. The choice is ours, what we want to do. Right? We are established in Him. Remember what the word established means? Established means to strengthen, to make firm. Right? You see in these colleges, big colleges, it becomes an establishment. Why? Because after, when they start off, they may be 10 students. But after 20 years, there are 1000 students. It becomes an establishment. We are established. We are made firm in Christ Jesus. Right? Again, we have an eternal purpose. We talked about that. Our purpose is not only here on earth, but our purpose is eternal to be with God. Chapter 104, the wisdom of God is upon us. Right? Now, this is very important, wisdom. When to speak, where to speak, how to speak, how to behave, how not to behave, what to do, what not to do. That's why the book of Proverbs is filled with wisdom. Solomon was a great king. He had a lot of money. He had a lot of wealth. He enjoyed things in this world. But in the end, what did he say? In Ecclesiastes, he says, everything is vain. Meaning, everything in life is going to pass away. Only God will remain. Everything else in life will pass away. Right? So, we need the wisdom of God. We need the God's wisdom to understand God's Word, to understand who we are in Christ Jesus. Okay, so let's move on. Yes, to all his promises. Okay, go to chapter 107. Chapter 107, we receive spiritual revelation. Everyone say revelation. You know what's the meaning of revelation? Something that is hidden is brought to light. When John, the Apostle John was writing his epistle of the letter of revelations, the book of revelations, he was revealing something that is yet to come. Right? That's what revelation is.  We don't always think in the natural. Is thinking in the natural important while reading the Bible? Do we have to think naturally? Yes or no? So, you're reading the Bible, you're reading, for example, the book of Daniel. Do you have to think naturally and spiritually or only spiritually? Naturally and spiritually? Why? Why must we think of both ways? Because the Bible itself is a book. This Daniel and Babylon, it is not, you know, some people who are not exist. They are real people. Babylon is a real place which Daniel went to. So, there is a natural, but there's also the spiritual. So, when you and I are reading God's word, we use our natural mind, but we ask God to give us spiritual revelation.  Right? So, even if we're reading, you know, the book of John or Matthew, Mark, Luke, John, we're reading that. What is it that we must do? We must think and understand and read, but also ask God, God, give me revelation to understand this. There are some things we cannot understand naturally. Can we? If you look at Jesus' ministry, he's walking on water. Can you understand that naturally? No. So, he said, God, give me spiritual revelation to understand that. Why did you walk on water? What did you achieve when you did that? You destroyed, you know, in the Old Testament it says that, you know, the rulers of Tyre, meaning the devil has us thrown on the seas.  He is God. He's able to do the impossible. Right? So, all of this, we need spiritual revelation. Yes? Jesus himself says, I have food for you to the disciples. He says, I have food for you, which I have so much to tell you, but you are not yet ready because you're still growing in the things of God. But you and I, now with the Holy Spirit inside us, we can ask God, God, bring revelation. What is unclear? Make it clear to us. Help us to understand. When I'm reading this, you know, when you're reading the scriptures, ask God, Holy Spirit, help me to understand. Bring revelation in this area. I'm not able to understand. Help me to understand. So, for example, you're reading the Old Testament. You're reading about the sacrifices and the offerings. Say, God, I'm not able to understand, but Holy Spirit, help me. Give me the wisdom to understand. And He gives us the wisdom. He brings revelation into our spirit. Amen? Yes? Do we believe that? Okay. Chapter 108, there is simplicity in Christ. The word simplicity is basically a person who's free from pretence and hypocrisy. Being simple, right? Not self-seeking, not, you know, not being proudful in life, but just being humble, right? Being simple, right? Now, in Christ Jesus, 1st Timothy 114, and the grace of our Lord Jesus was exceedingly abundant with faith and love, which are in Christ Jesus. 1st Timothy, sorry, 2nd Timothy 113, hold fast the pattern of sound words which you have heard from me in faith and love, which are in Christ Jesus. Now, living a Christian life is very simple. It is to live in humility. It is to live in obedience. Yet it is also to live in power and to live in authority. Now, you and I as believers must learn and develop the ability to balance both of these. Are you with me? Right? So, in one hand, there is humility, simplicity. On the other hand, there is power and authority. They are the opposites, but they go together as well. You see, Jesus is a lamb, but He is also the lion, right? He is a lamb who was slain, but He is also the lion of Judah. So, He was humble, but He is also a leader. Oh, great, with authority. So, as believers, we must develop this ability, right? We must know and ask God, God, give me, grant me this ability to learn how to walk in humility, how to walk in meekness, how to walk in simplicity, yet to walk in the authority and the power of God, right? And over time, as believers, you know, once we join ministry, once we are ministering to people, you know, you're serving, volunteering in church, we begin to understand this. Maybe some of you may become youth leaders. As you're working in that role, you will learn how to walk in humility, yet walk in power, right? Chapter 109, the blessings of Abraham, that is all the blessings of Abraham is upon each one of us, the Abrahamic covenant, right? So, there are old covenant promises and there's the new covenant promises. So, what, after the cross, it is not like the old covenant promises are done away with. Each one of us are part of the Abrahamic covenant, there's the Davidic covenant, there's the Noah covenant, right? So, all of these covenants are there and they're part of that covenant. What did God tell Abraham? I will bless you. You'll be a blessing to the nation and to the nations, right? So, that covenant is also for us. God said, I will bless you, right? So, we are part of the Abrahamic covenant, blessing in all things, blessed to be a blessing to the nations, righteousness by faith. How did Abraham have a right standing before God? Because he had faith in God. It was not because he was circumcised. It was not because, you know, he lived a good life. No, it was because of faith. Imagine God telling Abraham, take your son, sacrifice him. As he was doing that, it was righteousness through faith in Jesus Christ, through faith in God. So, we have righteousness through God and we have friendship with God. We have victory over the enemies. All the blessings of Abraham fall upon each one of us, right? Then we have the promise of the resurrection, 1 Corinthians 15-22, for as an Adam all die, even so, in Christ, all shall be made alive. We talked about this, yes? Adam sinned. After he sinned, what happened? What happened after Adam sinned? Sorry? Death came into this world. Sin and death came into this world, right? Death was not God's design. When God said, when he created the world, he didn't say death is one of them. Oh, when Adam sinned, death came into this world. But through Jesus Christ, when he died, he resurrected from the dead, each one of us will also live because Christ lived. Now, what if Jesus died on the cross and he did not resurrect? It's not a victory, yes or no? He took the sins, he died on the cross, but he doesn't resurrect. It's not a, it's not a, it's a partial victory.  Amen? The natural death, our physical body will be done away with, but we will, we have the promise of resurrection. We will all, as believers, we will live with him. Paul writes and he says, to be absent in the body is to be present with the Lord. So just picture this. As a believer, if a believer passes away, the next second, he's in the presence of God. Any picture of that? The next second, he's there. The promise of resurrection. Right? Now, the enemy may say, that's all a lie, it's not true, it's not there, there is no resurrection. How can you be born again? How can you live again? You may bring all those lies, but we have the promise. Is Jesus Christ alive today? He's alive? Then we, if we believe in him, even we will live. That's a promise. And then we talked about reigning with him and we acknowledge the good things that we have in Christ. Okay, let's go to the last portion. Let's go to chapter 115, Ephesians 2, 21 and 22. God's dwelling place. In whom the whole building, being fitted together, grows into a holy temple in the Lord, in whom you also are being built together for a dwelling place of God in the Spirit. We are God's dwelling place on earth. And so when we are living this earth life, we are to offer up spiritual sacrifice to God. Say this, I am God's dwelling place. Put your hand on your chest. Say this, I am God's dwelling place. Means God is living inside you. The Spirit of God is in you.  Each one of us must do our part to keep our temple, which is our body clean. I'm not talking about the physical cleanliness, but our body, our soul, our spirit needs to be cleansed. Just as how the physical body, we need to keep it clean, same way, the spiritual body. Remember, our body is a temple of God. As God's dwelling place, we establish God's presence in our community. Since God is in us, wherever we go, whether we are in college, whether we are outside, we may be in the workplace, we may be going anywhere to meet our friends, we establish God's presence wherever we go. So you may say, how do we do that? How do we establish God's presence? I'm not singing songs. I can't sing praise and worship songs in office. I can't start preaching in office through, but you are the temple of God.  You get what I'm saying? So if you're in the workplace, you can't take a guitar, start singing praise and worship songs. You can't say, I'm God's dwelling place. No, but the way you walk, your character, your life will emulate who Christ is. We de-establish demonic strongholds in our city. Since you and I are God's dwelling place, remember when we pray, when we get together in worship and prayer, we are dethroning the works of the devil. We are destroying the works of the devil. Yes? What did Jesus say? I will build my church and the gates of hell shall not prevail against it. Who's the church? The other church? So God is building us so that the gates of hell shall not prevail against it. So remember this, you may be sitting in this, in Bible college, you are spending time, supernatural hour, or in the morning, you're praying, you're spending time in worship. What is happening? You are involved in dethroning the works of the devil in your life, in others' lives, in the city, in the nation. That's what you're doing. As it may not feel it, but that's what it is, through faith, through faith. Yes? So there's one bread, chapter 116, one bread, one cup. Talking about the Lord's table, that we are one body. We drink of one bread. That is one body of Jesus and the cup, which is the blood of Jesus Christ. Right? So we are in covenant with God. We are in covenant with each other. Right? We are many members with many functions. Let's read Romans 12, 4 through 8, very important passage. Right? Now look at our physics, everyone look at your own body. In the natural, in your body, you've got many members and those many members have many functions. You have two eyes, you can't speak with your eyes, so you have a mouth. You have hands, your brain.  So it's an activity of the brain telling your body pick up the pen. So it's a simple task, but there are many things involved. Think of it, there's a pen here. Right? Now my brain firstly saying, I need a pen.  Now, even as I'm taking the pen, there are so many functions. I'm seeing the pen. I'm thinking about how to take the pen. There is so much. So just as our physical body has many members and many functions in the body of Christ, in the church, there are many members with many functions. Right? Verse 5, Romans 12, verse 5. So we being many are one body in Christ and individually members of one another. Having then gifts differing according to the grace that is given to us, let us use them. If it's prophecy, let us prophesy in proportion to our faith or ministry, let us use it for our ministering. If it's teaching, then in teaching. He who exalts in exhortation, he who gives with liberality, he who leads with diligence, he who shows mercy with cheerfulness. So basically Paul is saying, in the body of Christ, there are many members with many functions. Now picture this.  Are you plan to church? Now, can you do, can we start the church? We can start the church alone, but can the church function alone, only with you? No. You need singers, you need musicians, you need teams, you need volunteers, you need people who can become leaders, you need youth leaders, you need different, you know, cell group leaders. You need all of them, different functions, but you're building the same body, the body of Christ. Right? We are serving together. We are dependent on each other. We must honour each other, respect each other. And God has given greater honour to those who do not receive honour. Remember this always. In ministry, nothing is bigger and nothing is smaller. We have to complement each other. We have to support each other, encourage each other, respect each other and honour each other. So, we can have somebody standing in the pulpit, preaching in front of a thousand people and you can have a believer who is, you know, way at the back, setting up the chairs or in the welcome team. It may not be significant, but it is important. Both are doing what they're doing because it's a gift of God and they're doing it, serving together. By no means is the person who's preaching greater than that, than the person who's arranging the chairs or in the welcome team. All of them are the same. It's just the function is different. Right? You get what I'm saying? Right? The function is different. It's serving together. So when God sees you're serving, you're building the body of Christ. He's not going to say, Oh, because you preach so many sermons, you are greater. No. We serve together. We complement each other. So very important. I know most of you are young. When you are serving in church, don't look for only areas of, you know, where I can be seen and known. It's okay to start small. It's good to have a vision. You know, I want to become a leader or a pastor. That's good, but it's okay to start small. It's okay to start with the ushering team or just volunteering. It's all right. Think of the bigger picture. You are building the body of Christ. You're serving and we recognize each other in Christ Jesus. We collectively represent Christ. We collectively represent Christ. We talked about in section 12, we talked about ambassadors. Remember what ambassadors is? You know, for every nation has an ambassador. So what does he do? This one person will represent the entire nation. Right? Imagine you have an ambassador. He's going to the, you know, to a meeting where the leaders of different nations are there and this ambassador goes in with shabby clothes, chewing gum. What will happen? You think, hey, everyone in the nation are like that, disrespectful. They don't know how to, you know, be well-dressed or they don't know how to respect others because the ambassador is the one who will stand for the entire nation. One person for the entire nation.  Wherever you go, you are representing the kingdom of God. You're representing Jesus. Right? We have a heavenly call. Fulfill your ministry. Colossians 4.17. Let's read that and say to our compass, Paul is writing, take heed to the ministry which you have received in the Lord that you may fulfill it. Very important. Everyone say in the Lord. Your ministry and your service is in the Lord. It is for the Lord and it is to glorify the Lord. Right? Our ministry comes from Him because it is in Him and it is God working through us to fulfill everything that He wants to do. Never for a moment we must think that I have achieved all of this on my own. It is God, His power, His grace working in us. What does Paul say in the next portion? He says, He labored in the Lord. He worked hard. He put all His effort in. He says, I was shipwrecked. I was beaten. I was put into prison. I was defamed. I was persecuted. I was abandoned. All of this I went through. I labored in the Lord. Yet it is not I, but it is Christ abounding in my life. It is the work of the Lord. Yes, I labored. I did the physical work also, but all of that physical work will be of no use if Christ did not work in us. So there's this constant, unshakable and ever increasing labor in the Lord. Yes, we work hard, but we also say, God, it is because of you. It is because of your grace. The works that we do flows out of our life in Him, meaning whatever we do, the work, our songs we sing, the praise and worship, the teaching, the ministry, the evangelism, whatever we are doing, the teaching, prophecies, word of knowledge, the gifts of the Spirit, everything we do flows out from Jesus, flows out from the Holy Spirit. He is the source. If He is not the source, then whatever we do can be successful, but it will not bring eternal fruit. What do we need? We need eternal fruit. So, minister boldly in the Lord. Each one of us can minister boldly, must minister boldly. When we do that, we are doing it knowing that, hey, it's not my strength, it's not my ability, but God who's working in my life. So picture this. Somebody comes up to you and says, hey, pray for me. I want, you know, I've got this illness. Pray that God will heal me. Now, you pray in boldness. Don't say, wait, I need to go pray for half an hour and come back, or I'm not a healing evangelist. No, you pray because you know that you're not the healer, nor am I the healer, but God is going to heal. God is the healer. So you pray in boldness. What if healing does not happen? That's okay. You pray in boldness, minister in boldness. Right? That's why in the supernatural hour, we asked you to come and spare what God is ministering to you. Be bold, be confident. Don't worry. Right? I was surprised when none of you came up. Come on, share what God is speaking to you. It can be just a simple verse, but you need to step out. Be bold in ministering to the Lord. Right? Nurture people. We talked about ambassadors. And then section 13 talks about living the Christ life. We just go to page 112. We see that the spiritual and natural life of the believer. Very important. And we'll just go through this and we'll close for today. Right? Page 112, the spiritual and natural life of a believer. Now, there's a paradox. The word paradox means it is, it is truth both ways. So we are complete in Christ. Yes, Christ completed the work, but still we are a work in progress. That means God is still working in us. You see the paradox there? We are cleansed, but God is still cleansing us. We are perfected, yet we are being perfected every day. We are sanctified, yet we are being sanctified every day. We are hidden in Christ, yet we are visible to God. We are new creation, 2nd Corinthians 517. The old spirit has gone. We have become new, yet we are being renewed in our thoughts, in our words, in our actions, in our life. We are being renewed. We are righteous. What is righteous? What is righteousness? Right standing before God, right? We are righteous, yet when we fail or when we sin, we have to repent of ourselves. You see that difference there?  Paul says that, right? It's not I, but Christ crucified in me. We are possessing, meaning God has given us, he says, this is yours, and more is available, yet he says, you've got to press on for more. Right? You can say, God, I received so much from you over the last five years, but yet we are not satisfied. We keep drinking, we keep wanting more. It's like drinking water, no? Yes or no? We drink water. You can't say, yesterday I drank water, today I don't need. No, you need it. Same way, right? We are resting in Christ, meaning we know that God has done the work, we are in perfect rest, yet we are laboring for the kingdom of God. Right? So we'll stop here and we'll bring this course to a completion. I just want you to probably go back home and read those few more portions there, right? From 129 onwards, but it's, a lot of it is a repeat. What I will do is I'll post the assessments on the Google classrooms, right? And you can take help from others to complete that assessment, right? So let's just close in prayer and then we'll thank God for this entire semester and we'll close in prayer. Let's pray. Father, we thank you so much for this entire semester and the entire course that we studied. I pray God that you will continue to minister to each of us. Thank you for the deposit of your word and thank you for enabling us to learn and grow. God, I pray that each one of us will walk in this identity, this assurance, knowing that you are there with us, that all things have passed away and all things become new and we are in Christ Jesus. We come at each and every student at your hands. Those who are online, those who are here are God. And we pray God that we will continue to walk in this identity, walk in power, to walk in authority. In Jesus' name, we pray. Amen. Amen. Thank you, everyone. I had a good time teaching each one of you. Thank you to those who are online as well. God bless.


Welcome. Thanks for joining us this afternoon. My name is Megan Lindsay, and I'm the product manager for WebVR at Google. Today, I'm here to talk to you about WebVR. I'll show you the opportunities it opens up for web developers, how this is going to benefit the VR ecosystem as a whole, and what others are already doing with it. Then my colleague, Brandon Jones, will demonstrate how easy it is to build a cross-device WebVR app by doing it right here on stage. WebVR enables web developers to build fantastic cross-platform, cross-device VR experiences. Here's a quick overview of what WebVR is all about and an introduction to our recently released WebVR experiment site. VR should be accessible to everyone because it has the potential to let everyone explore, play, and create in amazing new ways. But right now, VR is pretty complicated.  And then when we want to play with their awesome VR stuff, we've got to have the right headset. VR should be easier so developers can make something quickly and share it with everyone, no matter what device they're on. Kind of like how easy it is to share stuff on the web, but with VR. Well, that's the idea behind WebVR. It's VR on the web for everyone. Here's how it works. Say you're in a browser like Chrome and you come across a WebVR experience. You just tap the link, put on a headset, and boom, you're in VR. Developers can build WebVR things the same way they build web things with JavaScript. And since it all works in a browser, it's easy to make it work for all kinds of VR devices, whether it's someone using their phone, their computer, or their entire room. Developers are already building and sharing awesome stuff with WebVR. We've started showcasing their work on a site called WebVR Experiments. It gives you a glimpse into the kind of stuff that's possible. You can play simple games, see the world in a new way, explore interactive stories, play with a friend, or lots of friends. Each experiment comes with open source code to help others make new experiments. And developers can submit what they make. All of this is an effort to make VR more accessible so anyone can build and everyone can play with awesome VR stuff. So come and start playing at WebVRExperiments.com. I want to tell you why we at Google care about WebVR and why we're investing in it. As Clay Bavor said in the keynote yesterday, immersive computing is going to change how we play, work, live, and learn. We're at the start of the next computing revolution. Many of you have seen the technology adoption curve before. 2017 is shaping up to be a pivotal year for VR where it's moving beyond innovators to early adopters. This is a time of opportunity. However, one of the largest barriers to even broader VR adoption and more user engagement today is content. Content is absolutely critical to the success of any new ecosystem. Giving users great, diverse, and plentiful things to choose from will keep them coming back. I believe that the open web is exactly what virtual reality needs to take it to the next level, and WebVR is the first step along that path. WebVR opens up VR to the largest developer platform in the world. You, web developers, you can build for VR for the first time. The web is an open ecosystem that we at Google strongly believe in and support, where developers from around the world work together to innovate in a standardized, interoperable way. The web isn't controlled by any one company, and it's unique in providing access to content from any device through any web browser. There are no walled gardens here. What this means is that WebVR simultaneously decreases the barrier to entry and extends the reach of your content. Using WebVR, you can start developing for VR with gradual investments by progressively enhancing your existing websites. You can light up your site with VR when an immersive experience adds something special, from breaking 360 news on the ground to exploring your next home. With WebVR, you can build your experience just once to reach all VR headsets and the billions of mobile and desktop users, giving you access to the broadest audience possible. And you gain all the benefits of the web by making your content searchable, linkable, and low friction with no installation required. Sharing is as easy as a link. So the potential of VR goes well beyond gaming. What kinds of VR content just makes sense to do with WebVR? Your imagination's the limit, though I believe the first wave of WebVR content will be the use cases that are already first and best on the web. Femoral content found primarily through search and social media. Short form media content and important, but perhaps less frequent tasks, where you may just not want to keep an app around. So let's take a look of some of the things that others are already doing with WebVR. Matterport has created technology that allows capturing real-world spaces in 3D to view them virtually for industries such as real estate, travel and hospitality, and architecture, engineering, and construction. Matterport customers like Sotheby's, Home Visit, and Mansion Global have scanned nearly half a million places and make these available to their users with Matterport's web player. The web player lets the user navigate through the 3D virtual space on their phone or desktop. Before WebVR, users were required to download a separate app to view the full VR experience. This created a lot of friction and resulted in significant user drop-off. But now with WebVR, this friction has been eliminated. The user can step right into the home they are looking at directly from the website. And when the user exits VR, they're still on the original website rather than in a separate app. Matterport supports WebVR for Daydream View and Cardboard support is coming soon. With over a million scenes created and posted by their community, Sketchfab is the world's largest platform to publish, share, and discover 3D content online. With WebVR, any Sketchfab model can be viewed and manipulated in your VR headset. Content creators or enthusiasts can use Sketchfab to share or embed models anywhere on the web, enabling them to be explored either on a 2D screen or in VR. Pauster creates custom experiences for movies and music, helping with the discovery of major entertainment products. With the rise of virtual reality, Pauster used WebVR for the broadest audience reach and created experiences focused on movie websites, showtimes, and ticketing. Here's a look at what Pauster has done recently. So movie studios saw over five times more movie theaters selected inside VR than on the regular websites. Audiences viewed the 3D trailer and the 3D gallery images, and they converted to seeing the movies in 3D rather than in 2D in the actual theaters. And finally, from filmmaker Christopher Nolan comes the epic action thriller Dunkirk opening worldwide this July. Just as the film offers a first-person perspective, Warner Brothers want a technology to offer a deep, immersive perspective on just what happened at Dunkirk. They brought this vision to life as one of the first collaborative VR experiences on the web, showing the depth of soldiers camaraderie through a cooperative experience between two people. Working together to survive the evacuation, each player will become both the rescuer and the victim. Here's a taste of what's coming for Experience Dunkirk. Experience Dunkirk will be releasing in June and will be open to everyone, supporting 2D devices as well as VR headsets. A teaser of the experience is live today, so check it out. Other areas we're seeing particular interest in web VR include news, e-commerce, interactive VR films, education, art, and custom business solutions. We are eager to see what web developers use web VR for next. So web VR content's arriving and web VR browser support is already here. In Chrome for Android, we've released web VR support as an origin trial for Daydream View and Google Cardboard. Our friends at Mozilla, Microsoft, Oculus, and Samsung have all released or announced coming support for web VR, bringing it to Samsung Gear VR, Windows Mixed Reality, Oculus Rift, and HTC Vive. In Chrome, we're continuing to improve and extend our web VR support. In our latest release of Chrome for Android currently in beta, we've significantly improved performance, making it more consistent and stable overall, and making it easier to reach target frame rates by adjusting rendering settings. We've also released web VR support for Chrome custom tabs, enabling you to enhance your native Android app with your web VR content too. Looking forward, we have support for desktop headsets in development. And we're bringing great web VR contract right to the Daydream home screen. Stay tuned for more on this soon. We've talked about progressive enhancement of VR content and how this is a superpower unique to web VR. Let's dig a little deeper into what that actually means and how others have solved it. Weather.com recently released an interactive web VR experience called The Birth of a Tornado. They applied progressive enhancement and responsive design principles to ensure their experience can be used on any device by optimizing the interaction model for the device being used. On desktop, you drag with your mouse to change the viewpoint and click to interact. On tablet, you change the viewpoint by dragging with your finger and tapping to interact. On mobile, the phone's accelerometer is used to provide a magic window into the VR experience. For Google Cardboard, head movement is used to gaze and target and tapping the button to select. And Daydream View uses the controller for interaction. Birth of a Tornado also works with Samsung Gear VR and the HTC Vive. The model used in Birth of a Tornado can be used with many web VR experiences. And we have a library to help make this easy that Brandon will show you a bit later. This is just one way to support cross-device experiences. Another example is Dance Tonight. Some of you may have experienced the Dance Tonight project IO yesterday evening, also built in web VR. Dance Tonight is an ever-changing VR experience made by LCD sound system and their fans. It's made entirely from VR motion capture recordings of fans dancing to a new song by the band. Another special thing about the project is that it works across devices but playing to their individual strengths. On desktop and mobile, you get to be in the audience. On Daydream, you're on stage.  If you didn't catch this in person, it'll be available online this summer. Your input choices and supported devices may differ for your web VR project, though we recommend starting with a goal of universal access as a best practice and just see how far you can go. While web VR content is still best experienced immersively in a VR headset, most people have still never tried immersive VR at all. Web VR content will be their very first hint of what they're missing. The great web VR content that you create will be the reason a new user decides to pick up their very first VR headset. I hope you're as excited about web VR's potential as I am. Now I'd like to introduce Brandon Jones. Brandon started web VR as his 20% project several years ago and co-authored the spec. Today, he's gonna build a cross-device web VR app for you live on stage. Please welcome Brandon. Thank you, Megan. So Megan talked about the principles of progressive enhancement. That is making pages that can be used on the desktop and mobile devices as well as across multiple VR devices. That can seem very intimidating, but the right tools can make it fairly simple. It all starts with creating some great WebGL content. WebGL is an API for rendering 3D graphics to the browser and is supported across all platforms today. There are many great WebGL tools and frameworks out there to help you bring your ideas to life. From there, turning your WebGL page into an immersive web VR experience can be as easy as adding a few lines of code. To show you what we mean, we're going to build a quick WebVR experience on stage today. The app that we're going to be building will be a 360 photo viewer, or a 360-degree photo viewer, which is a great fit for WebVR. These type of photos are easy to create with many cameras available that capture them and provide a fun experience that you don't get from traditional photos. Best of all, they can easily be viewed in 2D in browser with a click-and-drag or magic window controls while VR can optionally be used to provide an enhanced viewing experience for users with the right hardware. 360-degree photos also represent a class of content that's difficult to get users to install a native app for. Because of the content simplicity, the overhead of an install is probably enough to discourage most users, given that they likely only expect to spend a few seconds looking at each image. It's very likely that most users would never get past the app store link. Ideally, they could fluidly step into VR and out of VR with very little overhead, view the images quickly, securely, and then move on without having to uninstall anything afterwards. This sort of ephemeral experience is what WebVR excels at. So now we're going to switch over to the code and actually build the experience. Now, we're starting out here. Can we get the laptop up on screen? Thank you. We're starting out here with some boilerplate code. We're using 3JS. It's not the only framework that you could use for creating WebVR and WebGL experiences, but it is a fairly common one. There's also frameworks that are available that are expressly for WebVR content, such as A-frame or ReactVR. But because 3JS has fairly wide developer experience or fairly wide developer acceptance already, we're using that today as our example. Now, the boilerplate that we're starting here with is fairly simple, so I'm not going to cover it in detail. This is the type of thing that you would see in a 3JS tutorial of zero. And what it produces for us is a black screen. Well, that's okay, that's a great starting point. Thank you, that was awesome. So, because we're creating a 360-photo gallery viewer, we need images. Now, normally these would come from, of course, a database, a CMS of some sort, but we're just going to hard code them in for the sake of example. And then we need a way to view them. Now, because it's a 360 image, the method that we're going to use is to create a gigantic sphere, in this case, about 500 meters in radius. Invert it, and that's what the viewer's scale here is doing, is it inverting on the x-axis so that all of the faces point inward, and then keep the camera for a scene at the very center of that. That way, when you look around, you're seeing this sphere all around you that's practically at infinity. Next, we need to put our image on the inside of that sphere, using the 3JS mesh basic material. This loads up what's known as a texture in WebGL, and we'll apply it to the inside of that sphere, and it just so happens that 3JS's default coordinate systems work out really well for equirectangular images, which is the default that most 360 cameras spit out. Finally, we need to combine the geometry and the material together into a 3JS mesh, which is the basic primitive that it uses to render, and add it to the scene. So once we've done that, we can switch back to the browser and see that we now have a photo. Unfortunately, there's no interaction, so we can't tell that it's a 360 photo. We'll fix that by pulling in what's known as the WebVR polyfill. The WebVR polyfill is a JavaScript implementation of the WebVR API. It's targeted primarily at mobile devices. It uses their accelerometers to provide basic head tracking used for a cardboard style experience. It also happens to provide us with a basic emulated click and drag mode on desktop that we can use to get basic functionality on this desktop computer. Now, in order to make our application responsive to the WebVR polyfill, we have to add a 3JS extension called VR controls. We'll attach this to the camera, and then this makes it so that any head motion that happens on your headset is automatically applied to the camera itself. In order to make sure that it keeps updating with the head motion, we also need to add an update function to the animation loop. Once those two elements are in place, we now have basic click and drag functionality. And we can see that we actually now have a complete photo viewer for a single photo. But that's not terribly interesting. We want a gallery. So the next thing that we're going to do is provide a 2D version of the thumbnail gallery that allows us to switch between images. We'll loop through the image gallery that we had loaded up previously, load a texture for each, and then pass them to this add to gallery 2D function that we're about to define. Here, we're going to use a little bit of basic HTML manipulation to create a container div, add a simple class to it. I'll leave the CSS as an exercise to the viewer. Append the image that's associated with our texture to that container element, and then add a click handler. When we click on this thumbnail, we're going to swap out the texture on our gigantic viewer sphere with the texture that's associated with the thumbnail. And this will give us the basics of iterating through the gallery. Now, I should note, you can see that here, I should note that this is actually a terrible practice because normally you would want to use smaller images for the thumbnail to not impact loading time. But because we're doing everything locally here and for the sake of time, I'm skipping over that. But you can see here that as we click on each of the images, we can cycle through the various items in the gallery, and they're all viewable. At this point, the 2D site is done. We've done everything that we need to work both on desktop and mobile. But we're here for WebVR, so let's figure out how we allow people to dive into VR from here. The next thing that we're going to pull in is a utility called WebVR UI. This is a library created by the Google Creative Lab that provides a button that advertises WebVR support to your users. It will also communicate to them if they don't have WebVR support. In order to add that to our application, we need to go in, create an instance of the WebVR UI button, append it to the DOM, and then in this case, we're going to ask it what VR device it's associated with and cache that off for later use. If we switch over here now, you can see that we now have the button that normally would tell us that we can go into VR, but because we're on a desktop site, we can't actually go in yet. That is, we don't have the hardware connected so we can't go into VR here. We would be able to go on mobile and I'll switch over there in just a second. Now, even if we could go in because we have the correct hardware, we haven't actually wired up any of the VR rendering yet. We'll do that with another 3JS utility called VREffect. This makes it so that the content that would normally go through the renderer and show up on screen will actually be rendered twice for a stereo view. Using the correct parameters that it's going to query from the WebVR API. We also need to update the animation loop to make sure that we can properly handle when we're in VR mode versus non-VR mode. We do this by asking the EnterVR UI if the user has clicked the button and if it's presenting and if so, we'll render the scene using the VREffect. Otherwise, we'll render using standard 3JS render and then the last thing that we have to do is make sure that our standard request animation frame is actually using a VR specific variant if it's available. This makes sure that if we're on a desktop device where the VR headset runs at a higher frame rate than your average monitor, like 75 or 90 Hertz, we're running at the same frame rate. Otherwise, the user will experience a lot of stuttering in VR and come away possibly sick. So, we will update that. And at this point, we'll need to switch over to our Android device to see the rest of the experience. All right, great. So you can see on Android, we now have that nice magic window interaction mode where we're able to spin around and see the 360 photo without going into VR at all. This is great if you just want to showcase, one, that there's 360 content here because the user's natural hand motion will give them a hint that there's more to see. And two, just gives people a preview if they're, say, sitting on a bus and maybe don't necessarily want to blindfold themselves. However, once we hit the Enter VR button, we can now switch into VR mode. And at the moment, we're configured to use a cardboard device. And you can see that we would also get the nice stereo view. Now, these images aren't stereo, but you could render a stereo view of the scene. And it would work correctly in any cardboard device. So we've now created a basic web VR-enabled 360 image viewer. But once again, in the VR side, we've only done it for a single image. And that's not great. Especially when you're using mobile VR, you don't want to force the user to put the phone into a headset and take it out repeatedly in order to navigate between different elements in the scene. So ideally, we'd like to take the 2D gallery that we've created here and pull it into 3D to allow the users to select between the different thumbnails there. Now, this gets a little bit more complicated than the DOM elements, because we are dealing with 3D. So a lot more math is going to be involved. But the basics are still pretty simple. We're going to be using spheres, once again, just like the larger viewer, to represent the individual thumbnails. They're just going to be much, much smaller this time. And then down in, when we're looping through our gallery, we're just going to add items to the 3D gallery, as well as the 2D. That looks like this, which now we start to get into a lot of math, because it is 3D. Trig is kind of a part of the course. But skipping over the exact details of what we're doing here, once again, we're creating the texture to go along with the image. We're associating it with each of our thumbnail spheres. And then the positioning code here just puts them in a semicircle around the user's waist, somewhere that's kind of non-intrusive, but easy to reach. So if we switch back over to the Android, we should now see, yeah, we have this nice semicircle of the same thumbnails, once again. Now, this is cool, but that's probably not the experience that you want to leave your users with most of the time, because we're doubling up on the thumbnails in the non-VR version. So over in the code, we'll just add one more line to say, if we're not in VR mode, let's just hide the gallery. Makes things a little bit cleaner. So next up. Now, we've got the thumbnails, but we don't have a way to interact with them. And we're going to add that by using a library called ray input. Ray input is the library that was used by the weather.com example that Megan was talking about earlier. And what it does is provide a single unified model for cardboard, daydream, or higher end desktop experiences with six-stop controllers. In all cases, it gives you a cursor and a ray that are based off of whatever the user's capabilities are and uses that to cast into the scene, find an object, and allow you to click on it. So to start off with, oops, went a little too far. To start off with, we have to instantiate the ray input. We provide it the camera so that it knows where we're looking. We set size. That's just a little bit of bookkeeping. And then add the meshes that are associated with that into the scene. This is so that we can get the cursors that are associated with it in the ray itself. Like the VR controls, we also have to update this every animation frame to make sure that it stays in sync with the controller movement in this case. We also want to make sure that we know when we're actually selecting each of the thumbnails. So we're going to modify their opacity whenever the cursor is over the top of them. We'll start them out with a lower opacity. And then we'll have some event handling here that makes their opacity higher as the cursor hovers over them. One bit that I skipped here. We do need to loop through all of the thumbnails in our gallery and let ray input know that they are selectable. Otherwise, it will also try to select the larger sphere in the back, and that doesn't do us any good. And then finally, the last piece is that we say when we have clicked on whatever input, whatever the primary input is for our control mechanism, we're going to do the same thing that we did for the 2D gallery, which is swap out the texture for that thumbnail for the larger sphere. Now let's see how that looks on mobile. Well, let's save it first. Then we'll see how it looks on mobile. OK, so you can see, because I skipped over this, we no longer have the image spheres in 2D, but if we jump into the VR mode, and there we go, we now have a nice cursor that can swivel around and select the different spheres based on our gaze. This is, once again, a cardboard mode. And if we clicked on it, it switches the thumbnails. So now we have a fully functioning gallery that the user does not have to leave VR for in order to switch through images. Now, to demonstrate that this works correctly with more complex input mechanisms as well, we're going to come out here. Well, that's not what I wanted. Let's sync this up with a Daydream device. And then the normal part of the Daydream entry flow is that we have to sync up the controller, which takes just a moment. And then we should be back into our same experience. With now, you can see a basic ray-based selection cursor that does not depend on the movement of my head, but can still be used to do basic selection from the gallery. So that's it. In about 150 lines of code, we've created an experience that works on desktop, mobile, and VR, both cardboard VR, Daydream VR. And if we were to put that on some of the larger desktop systems, it would even work with an Oculus Rift or a Vive. So let's switch back to the slides. So to summarize some of the recommendations that we covered during the development, at this early stage, we should be focusing on apps that can be used in 2D with VR as an enhancement while the VR ecosystem is still growing. We should also strive to allow users to stay in VR for as long as possible, as frequently switching between the 2D and the VR modes can get a little tiring. Finally, there's a variety of input methods across all VR devices. And using library-like ray input helps normalize that into a single interaction model that's common between all modes. So now I'm going to turn it back over to Megan, who's going to tell you a little bit more about the future of Chrome and VR. Thank you, Brandon. Everything up to this point has been about bringing VR to the web. Now I want to talk about bringing the web to VR.   As we announced in the Daydream keynote this morning, we're bringing the full Chrome browser and the entire web to VR for Daydream View first. You can use the Daydream controller to navigate regular web pages and follow links. And for web VR experiences, you get transported into fully immersive worlds. You'll be able to watch videos in a large screen theater-like experience. Plus, Chrome and VR is the same app that you use for browsing in 2D. It shares all of your tabs, bookmarks, and history. You don't have to re-log in to websites and VR. Things just work. VR browsing is coming to Chrome for Android later this year. So what's next? Take a look at our web VR developer portal with some great tutorials and case studies and the helper libraries that Brandon showed us earlier. Check out the full set of web VR experiments online and consider submitting your own. You can also try out some of the web VR experiments here in person at I.O. in the experiments area. Thank you so much for joining us today. And I can't wait to see who you come up with.


In this video, we provide the solution to question number four from the practice final exam for math 1220 In which case we're given six infinite series here And we have to determine which of the following series are absolutely convergent Okay, so absolutely convergent means that if we take the absolute values of all the terms then it would be convergent in that situation So looking at the first one here the sum of one over the natural log of n well win The natural log when you are you're zero at one you're negative before that so starting at n equals two all the terms in this Series and the natural log here are already going to be positive. So one over natural log of n This is already positive here, but I should make mention that this series These fractions are going to be bigger than one over n So this series is going to be larger than the harmonic series, which is divergent So by the comparison test this one is a divergent series When we look at the second one here, it is an alternating series It is convergent by the alternating series test, but to be absolutely convergent We need to take the series of absolute values for which that just gives you the harmonic series Which like we mentioned a moment ago is divergent. So that's not the case there if you look at choice C We're just working by process of elimination. I can also notice that F is the harmonic series. So it's not that one When you look at choice C, this is a geometric series, but the common ratio is three halves Which is greater than one. So that'll be a divergent geometric series. You look at D here this sequence of factorials The factorial sequence is going to converge towards infinity not zero. So it's divergent by the test of divergence So by process of elimination We already have that the answer has got to be E because the other five cannot possibly be right But how could we convince ourselves? This is in fact absolutely convergent not just by process of elimination Well, if you take the absolute value of sine of n over n squared plus one Sine well, I mean because the denominator is already positive So the absolute value is really just playing a role in the numerator. Sine is negative sometimes positive other times, but regardless the absolute value of sine It's gonna be bounded below by zero but bounded above by one. So Our sequence is bounded above the absolute sequence I should say is bounded above by one over n squared plus one for which as n goes to infinity This is asymptotically the same thing as one over n squared for which now we're comparing ourselves to a P series which would be convergent by the p-test since p is equal to 2 So what we see here is that our series so this series as A p-series is convergent It's limit comparable to this series, which is convergent This series is larger than this series. I should say this series is larger than that series Which is the absolute series for this one in question here So by the comparison test this one would likewise be convergent and since the series of Absolute terms is convergent that means the series is absolutely convergent So we can find this out by process of elimination, but if you want a rigorous argument there Yes, this fact this series is in fact absolutely convergent


In our other videos, we've talked about emotion and specifically we've talked about Understanding emotion. What is emotion? How do we define it? Where does it come from those types of things? And then we've also talked specifically about what are some of the influences on our emotional expression But in this video, I want to talk about the next step. What can we do to improve our emotional expression? What can we do to improve our relationship with emotions in general? So if we're going to improve our emotional expression first, it starts with expanding our emotional vocabulary When your kid, maybe you had some of these charts in your parents We have you point to these things like how are you feeling or your teacher may have said point to the You know motion you're experiencing are you angry or you scared or you whatever, you know And essentially we need to kind of start with that, but we need to move beyond that You know, we know that for every emotion there are a variety of different Kind of shades to that emotion different levels of that emotion. So there's not just one word for angry, right? There's a difference between grumpy and frustrated and spiteful and irritated and offended and all those things As we can see here just these couple of words. There are a variety of different Words and that we can use to more specifically Identify so instead of just saying all the time. Oh, I'm angry. I'm angry. I'm angry What kind of angry are you and why let's let's expand that emotion of vocabulary So that people can have a more accurate understanding of exactly what it is We're feeling and what we're trying to express there. So we need to start by expanding our emotional vocabulary Once we've increased our emotional vocabulary, we can focus on then recognizing our feelings, right? We can we can identify those feelings more accurately. We can expand our understanding Of you know and and our vocabulary within ourselves About those feelings and about those emotions, right? We need to be better about Differentiating between the different emotions that we're having and our ability to recognize those And identify those and be be honest with ourselves about what it is that we're feeling what emotion we're experiencing I'm sitting to understand that we have the ability to experience and then to share Multiple feelings at once and we're not just limited to one thing You know if your friend is supposed to be at your house at eight o'clock one night and they don't show up They don't show up. They don't show up. They show up at like two in the morning And you haven't heard from them and you they didn't show up until you know much later You're entitled to feel a variety of different things when they finally do show up at your door It's okay for you to be angry. It's okay for you to be Frustrated with them for not being there on time It's okay for you to be relieved and joyful that they are safe That they are there you can experience all these things at once You can even express these multiple feelings that we sometimes get in this habit of saying well I've got to pick one and I've got to express it and I've got to stick with it No, it's okay for you to say look I'm super happy that you're here I'm so happy that you're safe and relieved But I'm also really frustrated really kind of pretty pretty angry with you right now for not contacting me and making me worry like that So we can share Multiple multiple feelings and we don't have to be just limited to to sharing one feeling at a time We can we can identify and express and share those multiple feelings We also need to take control of our self-talk right our self-talk has to do with How we talk to ourselves about these emotions. How do we how do we? In our own mind Experience those emotions we talked to another video about cognitively. How do we you know? What are our cognitive interpretations of an emotion when we experience these things physiologically and and and we You know have these emotions come upon us. They're triggered within us Then what do we tell ourselves about it? Are we you know and how long do we experience? So we let this thing kind of spiral out of control and and get out of our you know Reasonable control through without controlling that self-talk we need to take control of that self-talk And understand that we are in charge of our emotion now that emotion came to us because it was triggered by a specific event But we are in control of how we Express that emotion how we manage that emotion and a lot of that starts with how we talk to ourselves About that emotion and how we process it cognitively within our own mind We also need to accept responsibility like in this kind of relates back to controlling the self-talk But accepting responsibility, you know, we have this habit of saying Well, you made me feel this you make me so angry you make me so i'm nobody makes you anything Emotionally, I think and do things you don't like but in the end you are responsible for your emotion Nobody's made you do anything made you say anything made you feel anything They've done this thing you didn't like it or whatever But you are in control and we have to accept responsibility for For how we treat that emotion how we experience that emotion ourselves how we express that emotion with others And so we have to be in charge and accept responsibility for those emotions and We have to understand that not every feeling requires action Just because we feel something just because we feel an emotion doesn't necessarily mean we have to take action on it We want to process that emotion within ourselves, but it doesn't mean we have to tell everybody every emotion that we have Or really, you know Do something about every emotion that we have not every feeling or emotion requires an action If it does then we need to choose the best time and place for that Sometimes we get the feeling you know, we we get into the um into the habit of saying well this happens So I've got to do this right away. You know, it's if this happens. I have this feeling I've got to take action right now You don't have to do anything right now. You maybe you should maybe that's the right time in place But maybe not So we need to keep this process in mind that there's an event that happened that triggered an emotion or a feeling Within you right Then we need to think about that think you know process that what is this emotion? What's the best way for me to to manage and express this emotion? And then we can take action if if needed if we think that's required if we think it's appropriate And it may be right now is the right time to do that But it may be that waiting and cooling off or letting things settle a little bit or Waiting until you're alone with that person where you can express it privately or something Maybe better after we've had a chance to think about it and process it But we don't have to do things right now. We can choose What is the best time and place for me to? Express this emotion and follow up on that then So hopefully now we have a little better understanding of emotion not only what it is But how we can improve some things we can do to take more control of our emotion To manage them more effectively and productively and to use them more constructively and express them constructively within a relationship If you have questions about emotion or anything related to emotion and interpersonal communication Please feel free to email me. I'd love to hear from you in the meantime I hope that we will give much greater thought to the skill The skill set that really is emotion Again, we can't control what other people do and we can't always control what emotion that brings out on us But beyond that point we do have every control over how we experience that emotion how we express that emotion And so we can learn to improve our ability to both process and then express those emotions with great time and great thought and and more experience And and skill we can develop that greater emotional intelligence


Hello and welcome to JSA TV and JSA podcast, the newsroom for telecom and data center professionals. I'm Dean Perine, Executive Vice President of JSA. Joining me today is Mr. Mike Presico. Mike is the founder and CEO of ANOVA Financial Networks. Mike, welcome back to JSA TV. Hi, Dean. How are you? I'm doing well. I'm doing well. Mike, let's just go ahead and jump right in for our viewers that don't already know. Why don't you tell them a little bit about ANOVA? So, you know, if you look at it from a very high level sense, we're a carrier, right? Our services are set up that way. They're provisioned that way. They're consumed that way. I think we have two really unique differences. One, we have such a strong engineering bent and IP aspect that a lot of the standard carriers don't have. And furthermore, we're specific to the financial industry. So our MO is to connect every financial liquidity center globally. So whereas your cell phone, a tower is omnidirectional. It wants to serve every person. We connect the CME to the Japanese stock exchange. We connect European FX markets. And so that's the real distinction between ANOVA and, say, you know, a T-Mobile. And I guess by that reference, what you would say is you're a wireless company. And that's true. The preponderance of our services are of the mobile nature. However, we do still have a very strong fiber backbone to the extent that about 35% of our services run over that medium. It's where our background lied. It's where our origination came as a company. When I founded it, we were a fiber firm. But over time, we migrated to being predominantly a wireless service company for the financial industry. Lots coming out of your newsroom right now, even in particular, turning up a second channel between Chicago and New Jersey Triangle and making some notable improvements to the Aurora to CERMAC channel. Why don't you tell our viewers a little bit about those, the new announcements and enhancements? Sure. And, you know, if you think about it, they used to be all roads lead to Rome. And in reality, today for the financial markets, all roads lead to Aurora. Why? Because that's where the CME is. And the CME has a product, the e-mini product, e-mini S&P 500 that drives price formation in asset classes globally. So people want to get that price data to every corner of the globe. So that's why it becomes, for firms like mine, it becomes the epicenter of almost all of your networks. So when we add a channel from Aurora to New Jersey, that's connecting the CME to NASDAQ, to NISI and pushing this ES product out to people so they can consume it and then it affects the local markets. Same thing with Aurora to CERMAC. That is naturally the relationship between the products at the CME and the products that ICE have at CERMAC. And so it's a really interesting aspect to what we do where one location is from everything else stems out from that. And there's other pairs trading and things of that nature. But you can't go wrong building out from Aurora. You operate in a pretty interesting niche and you kind of always sat at the top of that niche too with regard to the financial kind of sector. But why don't you tell our viewers a little bit about exactly how ANOVA gives financial firms kind of a competitive advantage? Yeah. To us, there's a competitive advantage, but we look at it more so from democratization. And what I mean by that is we want to build a product that may be faster than the standard fair, than a common carrier. Their services aren't optimized from a point-to-point perspective and they're not trying to, right? They're not advertising it in that manner. So we build something out and it's faster than that. But then the goal is to give that to as many people as possible, small firms, big firms, new firms and level the playing field within our industry. And so it's interesting because there's a bit of a dichotomy. Yes, we are building low-latency services and yes, if you compare them to non-optimized offerings, they're faster. They have an advantage. But then the trick is to say, okay, how do I put this in the hands of as many people as possible to ensure that we're not dividing it into the has and have nots? That's been something central to our thinking all along, which is we don't want to build a product for six people, the six people that can afford it. We want to build something that the whole ecosystem of financial participants can utilize. And without going into detail, the biggest way we can do that is we distribute market data. Market data is one feed. Everyone gets the same feed. So while it's faster, just kind of in a generic sense, the feed that everyone gets, a five-person trading firm versus the largest proprietary shop is all the same latency. So that's how we like to accomplish our goals. Now, I love that. It's kind of a leveling of the playing field to give everyone a competitive advantage. I love the philosophy there. Thanks for that, Mike. But what's next for ANOVA? What can our viewers expect to see from you folks in the next, say, six months to a year? You know, when we first started out, we were a service provider and sometimes you strategically evolve. And then sometimes you kind of evolve and you didn't know it, right? And I think that that's how we became a hardware manufacturer, right? You know, it's just over time we accrued IP and assets that when you looked at them, you said, wow, I could actually, instead of buying off the shelf, I could put these disparate assets together and they could form the basis of a platform that becomes ANOVA's. And we believe that the more technology that you own, the more assets that you build and manage, it can be a real differentiator for your services. But B, it allows you to respond quicker to marketplace demands and changes because it's yours. You're not relying on some other manufacturer to implement something in your product set that they may not see a lot of value in elsewhere, right? And so that's what's happened to free space optics for ANOVA. And you may hear me say FSO, that's the acronym. And it's also, it's a laser. You know, since 2004, we've been sort of organically acquiring the technology to run our own platform. And I'm pleased to say that, okay, it's six years. I had initially planned for two, but six years. And we have a 10 gigabit per second free space optics technology that can go 10 kilometers. There's nothing else like this in the industry. And so this is going to be a real game changer for ANOVA. And, you know, you'll start seeing us beat the drum pretty heavily in terms of what it can do. Definitely have to maybe do this again here in six months to a year or maybe sooner, as you guys start beating that drum even louder. So, Mike, for our viewers that want to learn more, where should they go? So, ANOVAnetworks.com, all one word, plural networks, and also LinkedIn, Twitter. We're active on social media. And it's at ANOVA. So, for those that use Twitter, and that's, we're very easily Google-able, I would say. Outstanding. Mike, thanks so much for being with us today. I appreciate it. Great. Thanks for your time. You got it. And thank you viewers for watching JSA-TV, listening to JSA Podcast. We'll see you soon.


What's up everybody, Jason here for JasperJasperCaseBricks.com We just sold out this team random that helps Phillip select NBA 6 box picker team number 6 And again guys, it's your guaranteed a team, chance of the Warriors Raptors, Cap, Stunner and more So the way it's worse guys is just that you need a team random We have 13 spots, we'll take the names, randomize them only Whatever team you match up with is the team you get So number 1 matches up with the Warriors all the way down to the T Wolves And then, as an added bonus, we only sold 10 spots So if you bought a full spot in this team random, you got entered to win a free spot Top 3 get 1 each So the dice roller here will be for the free spot giveaways Right, we'll randomize these 7 names I bought in straight up Top 3 get a spot each, we'll paste them, that makes it 13 We use the same dice roller and we'll match you up with the team random list right there So alright, here we go guys Dice roll, 9 times 4 out of 5 So here we go, top 3 get extra spots 1, 2, 3, 4, 5, 6, 7, 8, 9 And 9 times, boom, 4, 5, 9 Kyle, Chad and Kyle, whatever, randomize it for you Kyle, dang Alright, so a little Kyle sandwich So let's paste your names there and these were the free spots So let's put a little plus sign there to show you guys what are your free spots there Now, 9 times again, this will be for the list of names Good luck, 1, 2, 3, 4, 5, 6, 7, 8 Boom, 9 times, 4, 5, 9 Kyle, your free spot at number 1 All the way down to Chad's free spot at number 13 But let's see how it played out guys, I don't actually know the whole order but Here we go So Kyle, congratulations man, you just got the thunder Chad, very nice, last bomb on Joe Cavs, Nicholas, get in the Raptors, Diego Woo, squeezing in and getting my thunder Giddy up, Chad get in the Lakers And then Kyle you got the Mavs, Nuggets, Sugar with the Grizzlies Lewis you got the Bulls, Daniel with the Pelicans Kyle with the Celtics, Lewis with the Nets And then Chad with the T-Wills So there you go folks, now in a separate video I'll have this pick a team through number 3 ready to roll and we'll get that going next And if you guys want to sell out number 4 We are just down to 1 left, so maybe we don't hit any big warriors hit Somebody will take them but that's the last team remaining in number 4 So I'm sure we won't need a filler for that We just gotta have someone step up to the plate and hit a homerun and take them So appreciate it folks, good luck everybody Next break is coming up Thanks for watching


I was on the bench, I felt like when I was on the bench they were, they were making plays and so I had sat back down and as soon as I got the pick I was, me and Todd were jumping up hugging so I was just happy we were able to see the win. By the time I got to him I was trying to talk but I was so tired running about 90 yards to get to him. I just told him great play and he's my brother man I was, I was just happy, just excited. This game is playing out like it's expected to end like that but is it playing out like the thought of which kind of physical affair where you know they kind of show us a fight to win it? Yeah I mean defense show, show fight, you know they never gave up, being resilient, making plays and doing what they need to do to be able to help us win the game and you know just probably those guys man because they work hard day in and day out throughout the week and you know just excited to see it all come together. Is this street kind of what I'm talking about? Yeah this, you know we just got to play competitive football and you know put all together you know on Sundays and you know no matter you know how it goes you know how we win I mean it's a win when we go to the win column so you know just enjoy this three wins in a row and it's hard to win in this league and I'm happy that we were able to turn things around these past three weeks. So it seemed like Washington was in it because they made their share of big plays you got yours when Nick came down with that ball that set you guys up and go ahead and touch down how big that you often stuck with it and found a big chunk play. Yeah that was huge, Nick getting that catch and making the big play and a big part of the game so yeah that was huge and we need more of that. You guys need this. It's just great as us, of course it emphasizes it every week and you know we want to get the ball to end zone so. You mentioned that, what is it? We're a team. I mean it takes all of us. I mean we're not playing, you know what I'm saying, point out individual. You know it takes all of us so we understand that. I mean that's just don't do that. It's collectively. You need a buy to have a good of the head in a moment. Have a good body week. Yeah I mean be good to let guys rest up and get their body back on them and then get some guys back hopefully you know enjoy the body week get away from the game and when the time to come back it back to work. The two screen sequence worked out pretty nicely with you and Don Trell. Yeah that was a lot of fun just happy we were able to make a play. I was able to catch a screen and get some yards and Don Trell got his way to touchdown so anytime we ever do that we're always happy. I mean that's always the focus and the focus on getting better and improving. No matter what the outcome is and continue to do that each and every day and I'm sure you guys get away a little bit but be ready to work and get better when we come back. How's my confidence though? I mean playing? I mean I'm gonna be me each and every Sunday so I mean me. Well man it's just you gotta find a way to win and we know how to do that and that's how sometimes it's gonna be in this league. Defend every blade of grass and guys came up huge at the end. I mean I think other than just to see what a defense was but not letting them score not when they need a touchdown. I mean I'm confident in what we've done down there in the past. That could change based on if they need a field goal. Paul I think that that's something that we talk long and hard about is if a field goal beats you I think that's a different story. But a touchdown we've just had too many stops down there and done too many good things down there. Is that what you're asking? Yeah. Sure. The players you know I mean the players and just being confident in what we're doing. You know I thought there was some you know some good calls down there they you know had them you know I think they were expecting one thing and clearly got another and you know almost had the interception there earlier with Christian. Well I think it's just getting back there into spots and you know something that we've been trying to work on and a vision and a break and you know we need more ball production more ball disruption. That's something that we're going to have to have on defense and this is a good place to start with you know with the game on the line. What do you have guys like? Yeah I mean those guys are great for us. It's just going to have to be better you know everything's going to have to be better. Those guys have been fantastic leaders for us productive players. I was proud of the way that Danico kept his composure you know and then Jeffrey obviously coming back and you know he apologized for whatever he did on the quarterback and then you know coming back and being able to help us. Well I think it's just you know we took it pretty good against Buffalo on a Monday night came back on a short week and you know we found a way to win three games in a row so I think that this bye week is going to be a great opportunity for us to catch our breath and get some guys healthy. We got some guys that play a lot of football for us just because they have to and you know we need to take care of them. Yeah I mean I was certainly not at what anybody wanted or expected or what we think that is standard you know that you got to take care of your quarterback only bad things are going to happen when he's getting pressured and hit. Their ability to stay in it hitting a big place what was kind of the messaging there in terms of staying in it to tackle and stay on top that was what the message was all week was you know not give up X plays and tackle and when they missed tackles led to points and X plays led to points. Same thing everybody else is thinking. Well I thought the protection there was outstanding I thought Ryan you know wanted to go to chag they came off Ryan climbed the pocket which was which was great and Nick Westbrook did what we you know need to do more of is go up and make a play on the football when it's in the air go attack it and make a play. I mean I don't you know we can't have them be under duress you know it's like you know we got to block them so we get some of these plays off you know we only take some shots I guys asked me about throwing shots so we got to figure out what we're going to do to take care of the quarterback and continue to do those things you know and the penalties hurt us you know the penalties you know we had some runs there that were you know really great runs and X play runs and the penalties hurt us there well I think that you know I mean we've talked about this before that there's banked reps you know reps that they've been running for April and then being able to put some scheme plays in and everybody understand them for that particular week so we need to do better before we get down there you know making sure that we're consistent in our ability to get down there to continue to produce red zone drives where we have you know scored touchdowns that's been the difference How much does it have to do? Yeah well I mean it helps you know I mean it helps but there you know some of these defenses there's guys there free and you know we did a nice job of covering them up and Derek was able to score you know I thought that their short yardage run was good I wish we could have been able to capitalize on that unfortunately that we couldn't but you know Derek you know caught the ball great I mean really nice catch on the screen fantastic you know catch to go and frame it and catch it out in front of his eyes turn and get up and produce you know change some field position and then Don Trill scored on the next play was Nate Nate was inactive he wasn't one of the eight though Lyman was it easy to call where you were going next or did those guys have a close practice week? No Dylan was prepared to go in there I mean we practiced that you know the red zone all week now they've moved me around a little bit you know from Mike to money and stuff you know so it was I was prepared for the play just the thing is you know we never panicked you know they made some plays you know we never played we know what type of players we got on the side of the ball so you know you never panicked just make a play everyone but this was my first one the year end you know just playing in DC and you know I saw some people out here and it was just a different type of feeling before the game you know I don't know I just felt good about today it was a tough one you know but we put it through it was just a relief man because the whole drive they was making plays we kept everything in front they got it balanced you know there was a penalty they got them close to the goal line the thing is you know we got to that point I'm smiling that I'm like you know this is what we built for this is what you dream of don't panic you know somebody make a play and we walk off the field you know it just ended up being me but it was a team effort it's hard to win in this league we gonna enjoy this you know it was a good one going into the bout week get some guys back you know healthy and just keep this thing going yeah I mean it's been good I mean you know some players you know get in let's experience some plays happen but the thing we teach on that defense you know just prepare like you're a starter you know the whole week just whenever your name is called just take advantage of the opportunity you know both sides of the ball those guys aren't going to make plays just how you respond to it it's so essential man like I said we practice a lot the red zone every week that was just an emphasis making sure as far as backside and the defense that we were playing I don't want to say too much just to be patient just let everything come to you early in the game me personally I got hit with some play because I was too aggressive you know just making sure somebody make a play you know get off the field yeah I was still out there I didn't leave the field I think I probably want to leave the field you know just showing love to the fans that was out there that came along with yeah I just think that just says a lot about us man hard nose you know blue collar and just never panic you know that just showed there you know over we can bring up a lot of games where it just came down to that last even this year you know it comes down to that last drive somebody has to make a play you know so offense you know made plays they got us some points on the board you know we just had you know finished it off you know we did it was a big deal man it was kind of flat in there you know going in so we was like the whole game like create our own energy you know especially on the field so you know we just feeding off each other you know trying to create that energy you know a whole game somebody make a play you know we it's flat let's get it back up you know just just constantly you know just keeping us our swagger you know in the game we believe in each other we're going to keep battling and find a way to win you know I think that's what has been proven in the last few weeks is we believe in each other we're going to keep battling no matter what's happened and ultimately find a way to win how big was the connection with Nick what did you see yeah it was huge play you know great play by Nick you know really kept us in the game there you know he had a post route the corner fell off late to Chick who was running a sail route I saw him late so I had to pull the ball back saw us one on one down the field safety had good leverage to take away the post but I knew it was one on one so it was basically just a trust throw giving my guy a chance to go up and make a make a play on the football and Nick made a great adjustment to the football and made the play for us yeah I just kept believing you know I think I've seen over the years here our defense is just going to keep battling and defend every bladed grass you know so I kept the faith and believed they were going to make a play didn't know what was going to happen who was going to make the play but you know David came up huge there at the end you know I couldn't really see I saw the back go out run the angle route coming back inside but then kind of went behind the old line I couldn't see anything and then all of a sudden David's running with the football so I don't know exactly how it all played out but great play by David obviously reading it out and you know coming up huge for us yeah no doubt it grows you know just believing in each other that we're going to find a way to win and winning is contagious you know so you get that taste you get that feeling you get that locker room after the game those are things that you never forget is celebrating in those locker rooms after wins and as the team gets a taste of that and starts feeling that it really brings you together as a team and that belief only grows so you know got some good things going you need to clean up some things but got some good things going and I just want to keep the foot on the gas keep going comes from the guys in the locker room you know I think you know this is not an easy game right it's a tough game and we got tough guys in the locker room you know I think it the message is sent from coach but it's guys in the locker room that believe in each other and don't lose faith you know keeps to the process of trying to get better each and every week you know we had a long season in front of us and we still do so we'll have to keep improving week in and week out you know we're just scratching the surface so you know it really comes down to the guys in the locker room believing in each other staying hungry each and every week going on to the practice field trying to take advantage of the reps that we get out there working together as a team and just steady improvement throughout the season yeah no doubt they did a good job of getting guys in the back field we knew that coming in that they're going to have a good front and they did a good job of getting pressure so I definitely have some things to clean up there but our guys kept battling you know on the one I had to pull back and get the ball down the field I had time to be able to do that pull the ball back and launch it so there's some good things in there too guys protected at certain times protected well so you know have some things to clean up but overall you know proud of the way our guys battled and we found a way to win three more touches it's huge we talk about it a lot you know we've been solid in the red zone since I've been here so it's something that we believe in we put a lot of effort and influence in I mean influence not a bad word intention we put a lot of intention into it something that we work throughout the spring, throughout training camp and obviously you know coming in each and every week trying to get a good a good plan together and then go out and execute it so we don't want to get down there these games are going to be tight and inevitably in the NFL most games come down to one score game so if you take a look at it you're going to score when you get down the red zone so there's a lot of belief that we're going to get down there we're going to score yeah back to back screens you know close to Todd for making those calls two great calls to get the ball they're getting a lot of pressure at that point early in the game so getting the ball behind that rush trying to take advantage of that speed rush and the guys made plays you know Derek obviously with the big run and then the second one there Don Trill had to get it on him quickly just because of the pressure there he was able to make a good catch and then obviously turn it up and score