It's March 2023. Welcome to the Teen's Cornerstone Connection lesson. In these series, we'll start off with lesson number nine. No laughing matter. Like seriously, it's not funny. With beautiful music from the orchestra, Asher on the tuba, Kiki on the trumpet, George on the saxophone, Kate on the piano and myself on the clarinet. Grace will take us through inspiring mission stories from the Eastern Central African Division. And of course, our panelists, Marie, Jabari, Misati, Ashley, and our wonderful Teen teachers. Enjoy. Hello, everyone. My name is Grace Waseke and I'll be taking you through the mission stories of this quarter. So, here's a spoiler alert. All the stories in this quarter will be coming from the country of Rwanda. And before I get into today's mission story, let me tell you a few fun facts about Rwanda. Rwanda is 26,338 kilometers squared. And this makes it the fourth smallest African country on the African mainland. The first three smallest countries being Gambia, Switzerland, and Djibouti. Rwanda has one of the youngest populations on earth. Believe it or not, the average age is 19 years old. The third fact, popular sports in Rwanda are basketball, football, and volleyball. And cycling, even though it was considered a mode of transportation, is now becoming a popular sport. And our last fact for today, subsitence agriculture is one of the, it's actually the main source of income for the Rwandan people. And their local staple foods are bananas, plantains, which they call Ibitoke, sweet potatoes, beans, and cassava. And with no further ado, let's get into today's mission story. Today's mission story is about a boy named Claude. And unfortunately for this guy, he became a habitual drunk when he was just 12 years old. So you may be asking yourself just how did it get this way? This is because he grew up in a family drenched in conflict. His dad and mom were always fighting. And the mom would many times fight with the mother-in-law. And whenever this happened, she would go back to her home and spend time with her mother. Many times she would plead with her husband to move the family to another city. But her husband always refused, saying that he didn't want to be far away from his kin. Now one day the father, Claude's dad, fell ill and he was taken to a nearby hospital. But after conducting tests on him, he was taken to a larger hospital since they weren't able to come up with any diagnosis. And when he was taken to this larger hospital and tests were conducted, they found out that he had malaria. He spent many days in the hospital and he didn't really do well. Many people thought that he was actually going to die. But instead of him dying, he started acting weird instead. So his doctor took him to a psychiatric hospital and then after quite a lot of treatment, he recovered. But the sad part about this is he was left deaf. So after going, you know, getting out of the hospital, he went home. But now instead of his neighbors rejoicing about his miraculous recovery, they started spreading rumors saying that maybe his wife had tried to poison him. This was the last straw for Claude's mother. So she decided to get a divorce. So she went back to her family and left Claude with his father. Then Claude's father sent him to his grandmother and later on he remarried and after that he sent for his son Claude to come back home. Now because of all this conflict in his family, this had really scarred young Claude and that's why at the very tender age of 12 he had become a habitual drunk. Now one day after having quite a few drinks and being absolutely tipsy, he saw his neighbor boy walking down the street with a book and this book was entitled The Great Controversy. But now the interesting thing about this book is that the binder had pictures of angels in white who are standing on the cover. Now this really intrigued young Claude because he definitely knew what controversy meant. He knew it meant conflict and he definitely knew what conflict meant. He'd seen it in his home a lot. So he wondered how can a book about conflict have angels on the cover? He was intrigued. So he approached his friend and asked him, what's that book? Can I know what it's all about? His friend looked at him and he saw that this guy is clearly drunk. So he did not meant his words. He drove straight to the point. He told him, if you repent you will stand like these angels on the cover. You will be able to stand before God on the day of his return. Now this this point hit home for young Claude and he instantly became sober and then he asked his friend. He knew that he was a seventh day Adventist and he went to church on Saturdays the Sabbath. So he asked him whether he could go to church with him and his friend was so delighted and he immediately said yes. So Claude went to church that Sabbath. He loved it there. Everyone was so friendly. The kids wanted to become friends with him. The adults were super nice to him. So he decided to go for the next Sabbath, the next Sabbath and the next and the next. And he started to read his Bible and since he didn't have any spiritual books of his own he would borrow spiritual books from his friends and he enjoyed reading them. Now in one particular book he read about a boy who wanted to witness to his friends about Jesus. So he asked his father, dad what can I do to spread God's word to others to my friends in specific? So the dad told him you can take some paper and write down your favorite memory verses on them and then give them to your friends. This Claude did immediately and in the course of time he did this for quite a while and in the course of time many of his some of his friends started coming to church with him and later four of them got baptized. What do you say to that? Right now Claude is 15 years old. He's in high school now and he still does that habit which is started once he accepted Christ. He still writes memory verses down on paper and gives them to everyone who may need one and he says that he loves God and he sincerely thanks him for forgiving him of his sin and that he will continue to spread his word as he gets himself ready for his return. What do you say to that? I hope you really enjoyed the story and right now let's get ready to listen to some music from our lovely orchestra. They're going to be doing song 601 Watchmen on the Walls of Zion. Did you know it was not God's plan to destroy the city of Sodom, Gomorrah and the other cities that were found in the plains of Mamre? Welcome to today's lesson Cornerstone Connections brought to you by the teens class Nairobi Central Seven Day Adventist Church and before I invite the panelists to introduce themselves I would like to welcome Misati for the opening prayer. Let us bow down for word of prayer. We thank you my father for your goodness for your love for your mercy and for your compassion. Mighty Lord we come before you this day and we seek that you may open our minds this Sabbath that we be able to draw closer to thee Almighty Father in just name we pray and we believe. Amen. Amen. So please introduce yourself. Let's start with you Misati. As previously mentioned my name is Misati Nyambani. Happy Sabbath and I hope you enjoyed the lesson. Happy Sabbath viewers my name is Marie. Happy Sabbath my name is Jabaji. Thank you all and a happy Sabbath to our viewers. Happy Sabbath. We would like to ask you this morning what do you know about the city of Sodom and Gomorrah? So to start with myself what I know about the city of Sodom and Gomorrah is actually that the names were never preserved until this day. In essence the names are derived from two Hebrew words that is Sdom and Amorah. Sdom to mean burnt and Amorah to mean a ruined hip thus indicating that which was done unto them. Sodom and Gomorrah was located at the south of the Dead Sea now known as Mount Sodom. Okay what else do we know about the city of Sodom and Gomorrah? It was not only Sodom and Gomorrah that were destroyed. At least five other cities were also destroyed. Wow thank you for that. And at the time the cities were referred to as the cities of the Jordan Valley. The land was fertile and beautiful. Wow. Other than being fertile the land also had beautiful beautiful vegetation. Palm trees, olive trees, you name it it was a beautiful land. And alongside that vegetation the flowers give out very sweet fragrances all year round. Wow. So do we actually believe that God was interested in destroying this beautiful city with fertile land filled with flocks? Would God really be interested in treating them so harshly and judging them so harshly? Well today's biblical story is a cautionary narrative and tale that really tells us the dangers of you know setting your house next to those who will give you the bad advice and it also just informs us that once that happens then then you know there are consequences to those decisions we make as humans. So we'll start with Marie. Please take us through the first section of the lesson. So the first section is the what do you think section and it states a catastrophe was going to happen in your town. Rank the following warnings from which you would want to be given first priority which would you want to be given last priority.  I personally would like someone to warn me first then I could warn the rest. Okay so what about the rest of us what do we think. Well I think that my friends should be warned already so they'll warn me. Okay what about you Jabari. I love to think about that. You'd have to think about that what about you teacher Bridget. I definitely want my family members to be warned first it would be so catastrophic to see them perish at you know at their own expense. So what I would do is I'd want someone to warn me first then I would take my pet then I would I would take my pet with me since I think I can't talk to the pet so let me just take my pet then I go warn my family then my friends then maybe I say city you know disaster is about to come. Okay so we want to now look at scripture and what it says Marie. What scripture should be looking at at this point? We should look at second chronicles chapter 19 verse 10. I'll ask Misati to read that. Yeah so second chronicles 1910 and the word of God expressly speaks. In every case that comes before you from your people who live in the cities whether bloodshed or other concerns of the law commands decrease or regulations you are to warn them not to sin against the Lord otherwise His wrath will come on you and your people do this and you will not sin. Any other scripture? And yes and teacher Bridget would you read Ezekiel chapter 3 verse 18.  Thank you so this tells us that it's our job to warn others us and all of us to warn each other. I'll give the example of when you catch someone doing something wrong if you leave them to do that wrong thing instead of let's say telling on them or telling them out then that you're in the wrong. Yes so that's very important we can see throughout our uh cautionary tale today about not that there's a lot of warning that happened because it is not God's intention for you and I to be destroyed. So we want to thank even the teens today for um joining us online today to do this to ensure that we warn the world that indeed Christ is coming again therefore we should prepare for His second coming and we do not get destroyed. We do not want to be amongst those the destruction. Jabari could you please give us a little more insight about this uh cautionary tale? Okay let's get into the story. The two angels arrived at Sodom in the evening. Lot was seated at the gate of the city. When he saw them he got up to meet them. He bowed down to his face to the ground. My Lord said, please turn aside to the house of your servant. You can wash your feet and spend the night there and then go on your way early in the morning. No, they answered. He would spend the night in the square but he insisted so strongly that they did go with him and entered his house. He prepared a meal for them making bread without teeth and they ate. Before they had gone to bed all the men from every part of the city of Sodom both young and old surrounded the house. They called out to Lot, where are the men who came to you tonight? Bring them out to us so that we can have sex with them. Lot went outside to meet the men and shut the door behind him and said, no my friends, don't do this wicked thing. Look, I have two daughters who've never slept with a man. Let me bring them out to you and you can do what you like with them but don't do anything to these men for they have come under the protection of my roof. Get out of our way, they answered. This fellow came here as a foreigner and now he wants to play the judge. You will treat you worse than them. They kept on bringing pressure on Lot and moved forward to break down the door but the men inside pulled him out, pulled him back into the house and shut the door. The men inside the house struck the men, young and old, at the door with blindness so that they could not find the door. The two men said, do you have anyone else here who belongs to you? Sons in law, not sons or daughters or anyone else in the city who belongs to you.  The outcry to the Lord against its people is so strong that he has sent us to destroy it. Yes and thank you for taking us through that. So what lessons are we learning from this this beautiful narrative that Jabari has read which comes from Genesis 19, very well delivered. Thank you so much. What lessons do you want us to pick from this story? Yes this question will go to Misati. Lot hesitates before obeying the angel's command to leave Sodom. Is this true obedience? Explain. So on this matter I don't see this as true obedience because true obedience is exactly what Abraham did. That is Abraham when he was told, I want you to leave your people. I want you to leave your land. Abraham does not in essence put unbelief. With the Lord for him he hesitated. He was like really are you sure? And I think this hesitation is further emphasized with the fact that his wife herself did not actually see Lot's urgency to the point that she was like okay how about I take a last look. Exactly thank you Jabari. Any other thing we should learn from this? Okay I have another question which will go to Teacher Bridget. If it is never wise to live close to people who are committing sin what should Lot have done? So this whole problem began when Lot decided to choose to live near the city actually within the city of Sodom and Gomorrah and it is a lesson to us that when we're choosing where to put up even later in life because right now we are teens we probably it's our parents who probably chose where they want us to live but even in future as we're thinking of where we want to live we need to consider what kind of neighbors we have. If you have a big basket full of bad apples and you only have one good apple the truth is that one good apple is definitely going to become bad unless you remove that one bad one good apple from those bad apples. So it's a lesson to us mingle with people who are pure so that you remain pure. Okay this last question is for Marie. Why do you think it is that Lot sands in law he didn't believe it? Well this week's scripture expresses a sad reality of Sodom and Gomorrah and why God destroyed them.  Well I think that seeing the beautiful city and seeing how perfect it was for them how comfortable it was for them to live there they had nothing to fear.  So how do you respond to God's appeal to you? I'd like to jump in right there and speak about my response to God's appeal. I think I feel at times that God is speaking to my conscience on certain matters that is when Christ calls us to be perfect even as our Father in heaven is perfect I see such a perfection as continuously responding beckoning in that God will pick some aspects in your life make you uncomfortable and then wants you to learn something and he won't stop until you learn that thing in that he will give you remedials until you pass the class. Thank you and I'll ask Teacher Bridget to read Acts 28 26 verse 25 to 29. Acts chapter 26 verse 26 to 29 it says for the king knows of these things before whom also I speak freely for I am persuaded that none of these things are hidden from him for this thing was not done in a corner. Verse 27 king Agrippa do you believe that the prophet do you believe the prophets? I know that you believe then Agrippa said unto Paul almost you almost persuaded me to be a Christian verse 29 and Paul said I wish to God that not only you but also all that hear me this day were both almost and together such as I am except these bones. Thank you as you can see King Agrippa was unsure he was almost saved but he hesitated. You can see this in Lot he his hesitation influenced his sons-in-law they were almost saved but they saw Lot's hesitation and were like no it's not going to happen. So are there those things in life that your you know God has called you to do but you're almost there and you're not quite there? You know sometimes we postpone our redemption for a later date. So what is that you're postponing? You know you you get convicted of a something like I need to stop this but you're like no I still like watching this so I'm not really going to stop besides I can still wait I mean I'm not dying today I will get forgiven I'll get saved I'll stop this thing a bit later and you notice this in king Agrippa he said you almost persuaded me but wait until a later season. So he postponed his redemption and you know the Bible doesn't even record where he came up and you know left the things of the world and decided to follow Christ he postponed his redemption we don't know whether he died the next day we don't know. Thank you for that what about you Misati? So I want to jump in right then I want to say that there's this aspect where the psalmist brings in presumptuous sin in that we know that what we are doing is wrong but then we see that God is this good loving compassionate father and we're like God cannot destroy me as in it's so small but of course that's what Ellen White calls pet sins see those pet sins which are so hard for us to let go of exactly what bring us down and at the same time I think it also comes with us misunderstanding God and I think that God wants us to actually express to embrace freedom that is and to express our love for him by obeying his commandments that's why Christ calls us to a more abandoned life and so I've had those things even on Sabbath Friday night Saturday that you know you're supposed to keep the Sabbath day holy but you're almost skipping it holy. Yeah so I'd like to just jump in right there and I'd like to mention that that is the best matches usually happen on Sabbath that is the EPL matches of course the best ones football all the sports practically and those actually are the most tantalizing matches the dabbies etc that is so your you know your cut up between should I watch should I keep the Sabbath day holy and you know for people like us who are not into sports we have our social media pages there are updates that are popping on your screen and you're wondering at that time you're in Vespers and you're wondering should I look should I should I text back should I respond or should I just keep focusing so you know such things you're almost keeping the Sabbath you're almost persuaded but once or twice you still find yourself in that set back where you're in Vespers someone's eating the fast and you're scrolling Instagram so right but this is no laughing matter the warning is out and clear that you know when the Lord calls you to obey the command you should and you may not get the chance like Lot did where the angels were dragging Lot and his family and they're kicking and screaming and taking all the time as they were getting out of the you know of the cities of destruction so it is time for us to heed to the warning and not operate on the almost mode how about we hear from teacher Bridget on you know one of the beliefs we have a seventh day Adventist yes absolutely so in the seventh day Adventist church we have 28 fundamental beliefs these beliefs are wholly based on the bible and they help us understand a seventh day Adventist what and why do we really believe what we believe so from today's lesson our fundamental belief is number 11 growing in Christ now the thing is if you think about it right from when you were born you are really really tiny but day by day moment by moment you continued gaining height length width right so in the same way just as God is interested in our physical growth he's much more interested in our spiritual growth and we're given three main pointers on how to grow spiritually number one is prayer consistent prayer constant consistent prayer number two is bible study private bible study and public bible study even as we are doing today and the last one is communing with other believers so that you continue growing and don't remain stagnant amen so let us please respond to God's appeal to us and really grow in Christ would like Ashley to take us through the romance chapter 12 verse 2 Romans chapter 12 verse 2 says do not be conformed to this world but be transformed by the renewing of your mind that you may prove what is that good and acceptable and perfect will of God and and this comes from the background of what were the sins of Sodom the greater sins of Sodom you know they heeded not the invitation of repentance and what is the invitation of repentance you know those things you get convicted of in your conscience when no one is preaching but you toss them aside and you're like not so important I mean it's part of life it's part of life those who profess to know Christ but deny him in the character and their daily lives if someone were to look at me today or look at you would they think no for a fact that you are a Christian and you reveal Christ both in your character and your daily life or when when when you first decided to be an Adventist to come to church was there this zeal that you don't have today you know such questions we need to ask ourselves and at times we take matters of salvation as trifles and light that they all but they all have an eternal consequence what we do today what we do now may not seem like has a lasting impression like I mean just for this moment and now but all these things have an eternal consequence and all these things weigh in the balances like you know the little things that you do here and now matter those habits you build today will be there with you for the rest of your lives and you know sometimes truth is unsettling but the fact that the truth is unsettling and it's not comfortable does not change the truth it's not changed by our discomfort or comfort it is just truth it is just plain whether it is live so dumb and go just imagine today I want to wake up and say Misati you're living home you're living your everything your pets your mom your dad and that's what God has called you to do would you do it I think you know I would want to test God you see Lewe Gideon tested God and he asked him that if this thing as he put a fleece right there outside and he said if this fleece is wet and the ground is dry okay then if this fleece is dry and the ground is wet then okay I would want to test God the same way to be sure it is God it is God exactly so you know truth is not changed but if if if we are called today to live behind our parents our everything and follow that is God has for us would definitely be hesitant that's true because you what you we most of the time say you know Lot's wife was not obedient she looks back but think about it this way you have children and they're in the city and the city is going to burn how dare you not look back yes but that's why God says it's no laughing matter today he calls you and I to make a decision to follow Christ and he has given us so many warnings and he's not going to rest he's not going to give up he's not going to say well you know my people you know they'll perish he is constantly seeking us and giving us the knowledge we need to just turn to him and follow Christ yeah so it's it's no laughing matter we should we should take it very seriously we should not turn back like Lot's wife did and we should not hesitate like Lot's did and it also calls for us then to as we deliver the news to others we also should deliver it with seriousness so that others may listen and actually follow so thank you so much for that we would now like to get into Matthew chapter 25 verse 40 I'll read Matthew 25 verse 40 okay it says and the king shall answer and say unto them verily I say unto you in as much as you have done it unto unto one of the least of these of my brethren you have done it unto me amen amen yes Jabari would you please take us through the Wednesday part okay one of the few bright spots in the story of Lot Sodom and Gomorrah is the theme of hospitality do you think Lot knew who is two mysterious guests wow when he first invited them to his home is it wise today to invite total strangers to your home in many cultures the form of hospitality showed by Lot is expected of all the people read the punchlines let's go through the punchlines and see which one each of us strikes the most okay so even as we go through the punchlines Jabari how about we answer the fact that you know what's your response to the fact that do you think that Lot knew who this mysterious guest was though no he did not know but I think he learned from Abraham because if you read the previous story Abraham met this same man afar off he did not know whether they were God he did not know but having lived with Abraham he knew like for the Jews and the Arabs even today meeting a stranger and giving them a cup of water is part of their tradition and culture so he might have just learned from Abraham and also the Bible records that it was dusk it was evening when this man came into the city knowing the area in which he lived knowing how those people look at how they wanted to deal with him at the door because he was not letting them out so he also knew that he does not live in a safe place so it would be necessary that this man come in okay you wanted to say something Misati and I think the thing is that with Lot for him he felt the need to protect this man because I think he had even seen himself firsthand what had happened to men who went into that city and then they stayed in the streets and it's interesting the way the Bible puts it that all men young and old in an I'm imagining in my head that there was a 15 year old guy who was there to see this man at the same time I'm imagining there was someone as old as say my grandfather there trying to see this man to see what is this that has come what is this has come into the city and what can I benefit from this exactly but in this case Lot is hospitable even his position at the gates you know he's like us standing you know outside the gate in church and inviting anybody and everybody to actually come in so that they worship with us yes teacher Bridget I'm afraid that that spirit of hospitality has really died down in this day and age yes because you realize that there's a lot of trickery so you're not sure if I invite this person is it a genuine person will they come and you know rob me of my property so it is a bit of a challenge however we're advised in the Bible that you know when you admit strangers into your house you might find that you've admitted angels to your house exactly so Sodom and Gomorrah were known to have the sin of lack of hospitality so today can we be caught up in that sin or are we caught up in that sin I think teacher Bridget has said very well how about in the church what can we do as teenagers in the church to ensure we are hospitable so one thing that truly we can do time and time again every Sabbath we get new members people who have never been to our church people who might not even be Adventists so as teenagers it is our responsibility to make sure that they feel hospitable they feel at home and they're welcome and we encourage them you know finding out during the week how are you doing how was your week here is the lesson kindly can you study it let's see you next Sabbath so those are some of the ways you can amen Maria I thought you'd talk about the teams together I was going to like when we had teens together in a Sabbath um after that I saw new faces coming consistently and people making friends with them which encouraged them to stay as well it's like good peer pressure wow yeah and yeah um yesterday I met I met Nakomita in the supermarket and he said to me that you know so many people after the togetherness are consistent because they are hoping for another togetherness where they get to meet so many people and many other teens who are in this and struggling together with them so it was something that was really good amen so back again to our title no laughing matter we are called upon to ensure we you know encourage people to join the kingdom you know so let's let's look forward to being more hospitable so that we can encourage more teens and more people to love the church all right so Jabai was taking us through the punch lines and really telling us which verse speaks to him you know the most okay for me it would be the viticas 1934 the foreigner residing among among you must be treated as your native born love them as yourself for your foreigners in Egypt I am the lord your god all right so why does this speak to you uh because sometimes as human beings we treat people differently as if we don't share anything in common with them wow okay thank you so much for that anybody else which verse speaks to you misati so the verse that speaks to me and I believe that summarizes a lot of what the ethos of our lesson is is Romans 12 22 where we are being called not to be conformed to this world but to be changed by the renewing of our minds in that we want god to do a neurosurgery on our minds in order for us to think different and thus be different amen amen what about you marie well I like Hebrews 13 verse 2 so it says do not forget to show hospital hospitality to the strangers for by doing so some people have shown hospitality to angels without knowing it I know like sometimes when we get a visitor like a random visitor I wonder why are they coming to our house but as my african mother does she will treat them so well like better than she treats us on some days and I was just I wonder but sometimes it's good it pays off it really does sometimes you're told to move from your room and your bed yeah and in convenience yeah thank god for your mother thank god okay anybody else uh ashley um that would be Colossians you want set your mind on things about you know where your mind is where your heart thoughts heart was inside them yes and how do we at times as teenagers pitch our tents towards sodom where do we put our minds so so lot was indeed a righteous person but the choices he made you know messed him up because he decided to live near sodom and also associate with the wrong people and that did affect his you know his thinking his actions were not as fast and quick even actually had to be given more grace to rest in one of the cities before they were destroyed um so thank you for sharing that um teacher bridge it would you like to also mention about a verse that speaks to you yes absolutely just like misati it's romance chapter 12 verse 1 and 2 yes that we should not conform to the things of this world and clearly we've seen in lots story that he actually almost conformed he almost conformed and the question that god is asking us today is um you know as as it was in the times of lot that the sites of sodom and Gomorrah were too good for them to live yeah what is preventing you from seeing god and from experiencing god yeah that's a rhetorical question you can think about it but what is making you feel like you want to conform and not to take part in god's god's work amen thank you for that would like to invite ashley to please tell us what the spirit of prophecy says in this lesson the spirit of prophecy directs us to the story of lot when he went outside the door and said to this man i have two daughters you see lot was willing to sacrifice his two daughters for the sake of this man and it talks about sexual immorality and it takes us to the story of betsheba and david and uraya in second samuel second samuel chapter 11 verse 1 to 5 and i'd like to read verse 3 which says so david sent an inquired story from verse 2 then it happened one evening that david arose from his bed and walked on the roof of the king's house and from the roof he saw a woman bathing and the woman was very beautiful to behold so david sent an inquired about the woman and some man said is this not but sheba the daughter of eliam the wife of uraya the hittite what was david doing he was walking on his roof one evening what is the scene of sodom fullness of red and idleness exactly what is david doing david was idle that is why he was walking in the evening on the roof remember at this time the israelites were at war as a king where should he have been at war at war but where was he idle in the roof in the roof walking walking that does not eliminate the fact that we also need time to sit down relax meditate go walking don't walk on the roof walk on the ground i think that would be safer but idleness that is how he got himself into this scene which he later which was ever before him and later he said my sin is ever before me creating me a clean heart creating me a pure right spirit within me that i may not sin against you because of all the sins that we could ever commit this is one sin that we commit to ourselves and even as much as you would think well i made this mistake and it's behind me it's not like stealing where you'd steal you stole something you returned it you got forgiven it's out of you sexual sin is the one you you know sin against your own body it will always be in your memory always no matter what you do unless god creates creating me a clean heart and in you a right spirit within me that is the only way of erasing these things so of all the sins this is the i would not say the most grievous but it's the sin that would affect the most okay and i'd like to jump in right there with this perverted they were not virgins they could not have been virgins and for that very reason it's a lot you know better so the men were scoffing at him you don't know what your daughters are doing behind your back and so for that reason they were like i we are not interested with i i refrain to use that word we're not interested in your daughters that is yes the choice of where lot lived really contributed to all this you know so the daughters then indulged in you know the the wrong things yeah so that does matter so how about as young people as teens what ways can you ensure you remain sexually pure what advice can you give others how do you remain sexually pure marie well i think you shouldn't be idle because yeah as that's what happens that's what the case was in most of these bible stories so always be busy with something something good right yeah idle mind takes you to those websites that you're not supposed to go to and i don't mind is a devil's workshop that i don't mind is a devil's workshop what other ways can you ensure as a young man you keep your way pure sams 1 19 verse 9 how can a young man keep his way pure um jabari yes and as jabari is getting it we can also hear from from you miss sati which other ways can you keep your way pure i believe there is like job speaks very empathetically on this and he says that i have made a covenant with my eyes i shall then why then shall i look last fully upon a maiden then david underscores that that i shall set no wicked thing before my eyes i hate the work of them that go astray it shall not cliff to me so what i would infer from this is just avoiding any situation that would actually bring compromising thoughts affections feelings and behaviors amen and you know in the world where we live today yes it comes from the people you least expect someone you think has the same standard with you may not necessarily so it is it may be awkward it is awkward at times but it is very important that you state your stand amen here and no further amen no laughing matter warn them yes jabari how can a young person stay on the path of purity by living according to your word amen so we must spend time soaked like teacher bridget said in the word of god that is the only way you're going to keep yourself pure yes teacher bridget i'd also like to add that accountability with each other is a very important aspect in remaining sexually pure yes have friends who will hold you accountable what were you doing why didn't you come to church last sabbath what were you doing have you been studying your lesson and the second and last thing i'd like to say is guard your senses as misati said guard your eyes guard your ears guard even words comes out of your mouth because that way in that way then you're going to um learn how to be sexually pure absolutely god actually had to save lot by grabbing him in and then what did he do with the people outside lined he blinded them so your eyes your eyes are powerful things yeah so let's let's guard ourselves and guard ourselves indeed from all this sexual immorality now i would like to ask teacher bridget um to take us through the last section yes so one thing that is quite profound from our lesson today is that god will fight and fight again until he gets you amen he will not stop he will not stop and we're learning that time and time again um destruction will not let us go until we all have an opportunity to be saved so we have a few verses to read just before we conclude so misati you'll take us through look chapter 21 verse 20 and 21 and then marie get ready with revelations chapter 17 verse 18 jabari you'll get ready with revelation chapter 18 verse 4 and ashli you'll get ready with mathew chapter 6 verse 24 so let's just get there and see how god is really struggling to ensure that we remain in the fold yeah so let me jump in with look 21 verse 20 and 21 and these are the words of the christ when you see Jerusalem being surrounded by armies you will know that it's the solution is near then let those who are in judea flee to the mountains let those in the city get out and let those in the country not enter the city revelation chapter 17 verse 18 state the woman you saw is the great city that rules over the kings of the earth and mathew 6 20 forces no one can serve two masters for either he will hate the one and love the other or else he'll be loyal to one and despise the other you cannot serve god and marie another voice from heaven say come out of her by people so that you will not share in her sins so that you will not receive any of her plagues amen so from this verse says we get to see that our lord even in this day and age he is warning us there's a destruction that is looming we ought to come out of Babylon we ought to forsake our sins or else destruction will come upon us remember that god loves the sinner but he hates the sin so at this time it is our time to separate ourselves from the sin or else the sinner will have to be destroyed with the sin may the lord bless you and we'd like to invite Jabari to do the closing prayer let's pray heavenly father we thank you for this day now as you are about to conclude our discussion maybe understand and internalize everything we've discussed and maybe live by what you've talked about this is my prayer in Jesus name amen


Welcome to this week's edition of Business in Hawaii. I'm Deilene Yanagida and we are broadcasting live from the ThinkTech studios in downtown Honolulu. If you want to tune in live, we are at www.thinktechhawaii.com and while there, please subscribe to our programs and get on our mailing list. The theme of Business in Hawaii is to share with you stories of local businesses by local people. Our guests share with us their journey to building successful businesses right here at home. And in the ThinkTech studio today is Shauna Christensen. Shauna is the retirement plan consultant with RBG, Retirement Benefit Group. Shauna, thank you so much for joining us. Thank you for having me. I have to admit that having you on the show is really exciting for me because of my passion for employee benefits. So if I could carry it away, just go ahead and take the conversation back. You can own it. Tell us a little bit about yourself, about RBG and then of course your passion. Thank you. I started in financial consulting, working with private wealth clients, those people who were in retirement and I quickly realized within about two to three years that I got defeated in my career working with these people because they hadn't saved enough. They were in their 60s, 65, even 70s. And I can't reverse time and get them to go back 30, 40 years to change their habits. So my natural progression went to how can I reach people early on? When they're in their 20s, they're 30s and 40s and the best place to reach those folks is in a retirement plan that's sponsored by a company. Now you can reach 20 people at a time, 30 people, 1,000 people and you can create good habits early on so that they're prepared for retirement. I think that that's probably one of the biggest challenges though, are convincing people that they want to save, right? And as business owners, we're wanting to be able to hire the talent that we need to make our businesses successful and at the same time we're competing for that talent and so we turn to employee benefits to sort of give us an edge on our competition and a lot of times that includes retirement benefits. A lot of working people now know that, hey, the competitive benefit packages offer some sort of retirement vehicle for me and so business owners are feeling that they need to include that. What are your thoughts about the trends? How do you see that moving or is it moving? Yeah, most employers do sponsor a 401K plan. Most of the larger employers. We see trends nationally actually where a lot of states are enforcing an auto-deduct IRA if an employer doesn't sponsor a 401K plan. That hasn't made its way here to Hawaii yet but certainly on the mainland that is forcing people to go, do I want a state-run IRA or do I want a 401K or some other type of employer-sponsored retirement plan. But I'm sure that's a similar trend here. Like you said, it's really hard to attract and retain and keep good talent so people do need to offer some sort of retirement. So I'd love for you to share with your viewers about perhaps I'm a new business owner and of course I'm going to have some employees and want to be able to offer that benefits package that will include a retirement vehicle. Tell me, walk me through the steps. What do I need to know or what do you need to know in order to get me going? You always want to know the goals. And we're assuming here the goal is to attract and retain talent. So figuring out what type of vehicle you want to offer to your employees is important. Most people just default to a 401K but there's three, four other types that you can choose as well. That might be a little less cumbersome. So it depends on how many employees do you have. What is your budget? Do you want it to be employee only deferral? Do you want it to be have a company match? Do you want to have a vesting schedule or not? Some of these types of plans are always 100% immediately vested. Some are employer funded only. And like a profit sharing plan you also have a SEP which is those to our employer funded only. So there's a lot of decisions other than just let's go with the 401K. Four enclaves are the most flexible but they also come with a lot of rules, regulations, and costs. Wow, OK.  And as a business owner why I really don't know. And when we talk about goals, I mean of course I'd like to offer great retirement benefits. But what's in it for me? What's in it for you is attracting and retaining talent. One of the main things employees say when they come, it's obvious you're going to have health care benefits. That's a very obvious one. But with unemployment rates where they are right now, you need to do more than that. 401K is another obvious one. There's other benefits and perks popping up like student loan repayment programs. So employers are getting more and more creative in the programs that they provide. 401K being a very obvious one. So I'm going to go to my retirement plan consultant. Thank you. And I am going to ask you, well, how do I get started? And by offering a 401K because somehow that's the buzzword or the marketing that is gone out that I should offer a 401K. Are there any tax incentives for me in doing so? Or are there any benefits for me? Yes, there's tax incentives for you. And there's tax incentives more importantly for your employees. If your employee base is going to be high earners, you want to have a 401K, so maybe they want to max out. And they also want to defer taxes in the current year. But another important consideration is for young people coming into the workforce, one feature that isn't broadly available in 401K plans is the Roth feature. And that is a very, very powerful tool for young people because what it does, it allows them to pay the taxes today when they're just starting out in their career, allow it to grow tax-free. And then when they take it out, they have a big tax-free bucket of money. But that is not communicated well to your young folks. The power of a Roth in a 401K plan. And I think it can be better communicated. Are you finding that communication is the reason why there's not a lot of awareness? Absolutely. Employees don't come in asking for a Roth. They don't know what a Roth is. Do you know what a Roth IRA is? Roth 401Ks only came out in the last six to 10 years. And it's not well communicated to people. The record keepers don't promote it. It might take an amendment to add it to your plan. So I think people can shy away from doing work on your plan unless you know how to get them to do what's in your best interest. And more importantly, your employee's best interest. How much will it cost me to start one up? To start a 401K? How many employees would you have? Say, I have just one or two. OK. It's about $2,500 on the administrative side. But then there's costs that your employees, so that's your cost as the business owner. There are tax incentives for starting a 401K plan. But then there's also costs that the employees bear, which is important to understand as well. So if I offer a 401K plan to my employees, there's a cost to them. It's not just a retirement plan that I offer to them? No, there's definitely a cost to your employees. And if you do ask any employee, what is I have a 401K plan? What are my costs? Everyone in the room will say that I don't pay anything. And there's a couple good and a couple bad reasons for that. The cost can be hidden in the cost of the investment option. And they don't see the cost explicitly on their statement. So do most small businesses try to find a retirement plan consultant and just start up a 401K plan like that? I mean, I feel like there's so much we don't know, but yet we're trying to buy this product, right? So what are the steps that I need to take to do that? What should I be aware of? I feel like there's too many things unknowns for me. Yeah. So in terms of where do employers go when they're thinking of starting a 401K plan, one obvious place would be their private wealth manager. And they go, hey, I just started this business. Or I have this business. Can you help me with a 401K? That's one spot. Another place that people go is to a TPA. There's a lot of great TPAs here locally. Many of them very well known. And so they reach out to the TPA and say, hey, you can help me set up my 401K plan. And then other people go to more of the nationwide brand names like Fidelity and Vanguard. And they'll just call Fidelity or Vanguard direct and say, I know you guys do 401Ks. Can you help me? What is a TPA? OK, a TPA is your third party administrator. They're the one who's. So every 401K plan, just like we as individuals have to file a tax return, every 401K plan has to file a tax return as well. So they do that. That's part of the administration. The second part is, in order for a 401K plan to be tax qualified, meaning you can reduce your taxable income today and maybe pay the taxes later, you have to do certain discrimination testings, guidelines that the IRS puts out for you. And you have to pass those discrimination testings to keep the plan qualified and to make it run smoothly. So that's your third party administrator. When you say discrimination testing, what am I discriminating against? So when the tax code came out and the IRS was going to allow people to reduce their current year taxable income, which is a big benefit to business owners and is one of the big reasons why a lot of business owners start a 401K, the IRS said, well, we don't want you to just, because we're giving you this tax benefit, we want to make sure that you make this a benefit that's good for your employees. So they put in certain rules. There's about five discrimination tests that you have to do. One of the most basic ones is the average deferral percentage test. And to put it simply, the IRS defines a highly compensated person as a business owner or someone who makes more than $125,000. So you group those people together. Then you take the non-highly compensated people, anyone earning under $125 and not an owner. And the average savings rate for the highly compensated people versus the non-highly compensated people cannot be more than two percentage points. What this does is it encourages the employer not just to set up the K plan for himself. It says, you need to go get your employees into the plan. You need to encourage them to save. You need to teach them how to save. So that's one of the basic tests that they have to do. And I've stated that very, very simply. The rules are a lot more granular. But that's the very basic explanation for it. You've already shared overwhelming information with a business owner who's starting out and wanting to offer a 401K product. And you had mentioned that there are different parts to setting that up. We are going to go to a quick break. But when we come back, let's finish up that conversation about the TPA. And then anyway, you'll tell us all about it. Thank you, Dave. We are going to take that short break. This is Business in Hawaii. We'll see you back here shortly. Aloha. I'm Keisha King, host of At the Crossroads, where we have conversations that are real and relevant. We have spoken with community leaders from right here, locally in Hawaii, and all around the world. Won't you join us on thinktechhawaii.com or on YouTube on the Think Tech Hawaii channel? Our conversations are real, relevant, and lots of fun. I'll see you at the Crossroads. Aloha. Hi, I'm Rusty Kamori, host of Beyond the Lines. I was the head coach for the Punahou Boys varsity tennis team for 22 years. And we're fortunate to win 22 consecutive state championship. This show is based on my book, which is also titled Beyond the Lines. And it's about leadership, creating a superior culture of excellence, achieving and sustaining success, and finding greatness. If you're a student, parent, sports or business person, and want to improve your life and the lives of people around you, tune in and join me on Mondays at 11 AM as we go Beyond the Lines on Think Tech Hawaii. Aloha. Welcome back. This is Business in Hawaii. And with us today is Shauna Christensen of the Retirement Benefit Group. Shauna, when we left to break, you were explaining to me, as a new business owner, if I wanted to stand up a retirement benefit for my employees, perhaps a 401K, that there are parts, specific parts that I need to have in place in order to make that work. The first that you were explaining to us was the TPA. You were mentioning very similar to individuals. Retirement plan needs to file a tax return. Tell us more about the other parts that I need to have in place. So the second important part is your record keeper. So that's the one you'll recognize as the Fidelity Vanguard Empower, John Hancock. There's a whole bunch of them out there. What the record keeper does is they receive the contributions that you withhold from the employee's paycheck. And then they invest it based on how the employee would like to invest their money. So they record keep that whole transaction. The record keeper is also going to be what your employee sees as the 401K. The employee isn't going to think about your TPA, the third party administrator. They're going to think Vanguard, record keeper, because that's where I log online. That's where I keep my data, my beneficiary, all of those types of things. And is there a third party in that? Absolutely. The third party would be your consultant or your advisor. And this is a very important role to a 401K plan, especially for a small business owner where you are not fully aware of all the risk of rules and regulations. Your advisor, most people think of their advisor as, oh, they help me take a look at my investments and maybe they'll come in and educate my employees or help them enroll every once in a while. Your retirement consultant should be the one that helps you holistically look at the plan to help you monitor your other service providers. Are they doing a good job? Are they charging a fair fee? Is it reasonable? These are things that employers, especially in small companies, where you have the controller who's wearing five different hats, the owner who's wearing 10 different hats, they don't have the time or the attention to really monitor those other service providers to make sure that they're doing a good job. So I'll bet that each one of these three folks that are going to work for me to help me provide this retirement benefit, everybody's got to get paid, right? Do I pay them as the employer or perhaps could I get my employees to pay for some of that? You could get your employees to pay for everything, but most employers pick up the third party administrator's fee, which as I mentioned earlier, baseline is about 2,500. The more you grow in employee count, there's typically a per head charge. And that fee is, I'd say 90% of the time, even 95% of the time paid for by you, the employer. What isn't paid by the employer and which is typically paid by employees, whether employees know it or not, is the record keeping fee and then the advisor or the retirement consultant fee. And those are typically charged as a percentage of assets. So if there's a million dollars in your plan and your advisor's charging 50 basis points or half a percent, they're getting $5,000 on your plan. But it's not, there's a fee disclosure that you can go collect and look at it, but it's not explicitly stated as a line item on an invoice. So those fees can very much go by the wayside and go unnoticed. As a business owner, should I feel that I have the ability to negotiate some of those fees down? I mean, do I try to negotiate a TPA fee down? Do I try to negotiate a record keeper fee down or are my consultant fee down? What do you think about that? It is absolutely your duty to negotiate and make sure that the fees are reasonable, especially the fees that your employees are paying. When you sponsor a 401K plan, under the rules of ERISA, you are a fiduciary, which means you have to act in the best interest of your employees. You can't put your interest ahead of the employee. You can't put the record keeper, your advisor. No one's interest can come above the employees, which means you do need to, even though you don't get invoiced for the fees your employees are paying, you need to know what they are and you need to benchmark them. So go out to a third provider and make sure that your fees are reasonable, at least once a year, I would say. So going back to this consultant, would that be a financial advisor? Yes. Would my employees be able to ask you an independent question about their finances, so their investment strategy, or what have you, and are you able to help them and tell them what they should do, what they shouldn't do? Absolutely. Now, every advisor's service agreement is gonna be different. So pull the service agreement from your advisor. But if I were you, the plan sponsor, or an employer who cared about his employees, I would look to my advisor not only to help them save for retirement, choose how much they're gonna save, educate them on the risk and return profiles of the investment, so they don't make bad choices on their own. But most good retirement consultants will go much further than that. A lot of times one of the biggest barriers to an employee even saving for their own retirement is they're straddled with so much cash they can't even save. So a good retirement consultant will go back to basics for those folks and take the time and care to help them with other financial stresses that are preventing them from saving for retirement. So one of the things that perked my ear up is you said, well, if your plan has a million dollars in assets, well, my plan will likely not have a million dollars in assets anytime soon. But what does that mean for me? And how does that affect the pricing and what should I look for? I feel like there is some sort of strategy that I should be employed with to go out and manage this plan. So when you're looking at the fees an employee pays, it's typically paid in two ways. One is like I mentioned, like an asset-based fee that half a percent, that maybe the advisor charges and they charge it to assets. The other way that employees are hit with fees is in the investment cost of the funds that they're invested in. Now, when you dissect the investment cost of those funds, a lot of retirement plans have behind the scenes revenue sharing. So let's say you and I as an employee invest in XYZ fund. It has an expense ratio of 1%. If you look, if you open up the hood of that fund actually just request your participant fee disclosure and your plan level fee disclosure and it'll all be laid out there. But there's revenue sharing that goes from the fund back to the record keeper and even back to the consultant. So while you might think the consultant is making half a percent on assets, you might be getting a little more juice for lack of a better word on the backside from the funds. So you really wanna look for lowest costing funds and try and strip that revenue out so it's much more transparent for the employees. Okay. So I know that I'm gonna have you back on this show numerous times because I've got a ton of questions for you. But when we're initially talking, we're talking about how business owners as the very first step, if they already have a retirement plan set up, a 401k plan set up, that they can take a look under the hood if you will. But even if they're not really versed in it, what are some of the things they should look at?  But just about every record keeper, the TPA's fees are normally fixed and by the way it's the employer paying it. Well you really wanna, where fees get out of whack? Because you see that invoice from the TPA. You can monitor that. Well you can't seize the fees in the plan which the employees are paying so you don't feel it as a business owner. But it is your duty to make sure those are reasonable. So every record keeper when they start you up, there's certain break points you can take advantage of. One of the most common first break points in a 401k plan would be once you reach $500,000 in asset. You might see a reduction in fee of about 10%. But you can't realize that unless you go to the record keeper and say, hey I reached my break point, lower my fee. And then there's break points from there, 750,000. A million is a very often common one. I think from there you would see three million once you hit assets there. And your advisor's gonna have break points too. So make sure you know what your advisor's break points are as well so that you can, as your assets grow and your employees are building wealth, one of the best ways to give them additional returns and compounded returns over long periods is to take advantage of those break points as you hit those milestones. Two questions. As an employer or a business owner, do I rely on my consultant to help me understand where those break points are? You shouldn't be able to, but not all consultants are monitoring fees, especially so there's two consultants you can work with. One consultant who's gonna be a fiduciary with you and you can count on them to help you monitor fees because they're on the same side of the table as you, they're liable like you are if they don't monitor, help you monitor fees. And there's another type of retirement consultant or an advisor who is not a co-fiduciary or a fiduciary in any sense of the word. So it's not their best interest nor are they legally bound to monitor the fees and make sure you take advantage of those break points. So you really wanna first identify what type of advisor do I have? And lastly, either advisor that you do have, the final responsibility is always on you. You can never give up full responsibility and you're the last person the DOL IRS will come to if you're not monitoring fees or doing what's in their best interest. So the responsibility always lies with you. It makes sense to offload that if you can to someone who wants to take that same responsibility with you and will help you with that. The second question was as an employee, is there someone that I should be relying on that can help me understand break points and pricing and all of that? If you know who the advisor is of your 401K plan or maybe a good exercise for you the next time your record keeper or your advisor comes in to do an education workshop, be it an enrollment workshop, whatever that is, if you're sitting in that classroom I encourage you to raise your hand and ask the question, what are my fees? Participants don't do it enough, you need to do it. And so I would strongly, strongly encourage all employees part of a 401K plan, let's all raise our hands and say what our fees are because I guarantee you you can get a lot of fee reductions just by asking the question. I like that as a takeaway. So just to recap, the takeaway for our audience today is to ask what are my fees? What are my fees? When's the next break point? When's the next break, yeah, got it. We want to make sure to have you back over and over again and each time we'd love to hear our newest takeaway so I'm gonna go back now and ask about break points and fees. And is there anything that you'd like to leave with our audience today? And of course, please tell them how they can find you. Know what your 401K is as a business sponsoring a 401K plan. Know who your service providers are and make sure they're doing a good job for you. Ask the questions about fees. I'm with Retirement Benefits Group, as you've mentioned before. We have an office here in Honolulu off South King Street. So please visit our website. Come and visit us anytime in our office. Send me an email, pick up the phone and call. If you're having trouble identifying what your fees are, we're happy to help. Awesome, thank you Shauna. Thank you so much for having us. We are out of time. I'd like to thank Shauna, RBG advisors, of course, the wonderful production staff here in the studio. If you would like to be a guest on our show, please subscribe and leave a comment below. Business in Hawaii airs every Thursday at 2 p.m. and we look forward to seeing you here next week.


The benefits of using songs and music for warm-up activities. Although all parts of a lesson are important, the engage phase, or warm-up, may be the most important. The engage phase is the departing point of the lesson where you need to draw the attention of the students away from other occurrences of the day and make them focus on learning the English language. Choosing an activity to grab the student's attention can be a challenge, as it needs to work within just a few minutes. Through various studies, music has shown to be an activity which utilizes many parts of the brain at once, and therefore is a great activity to jump-start the brain, and get students to focus more quickly. Why music activities are great for language learners. Music can benefit a classroom environment in many ways. Most and foremost being that music, in general terms, is something that is enjoyed by more or less everyone. It can help students to be calm and relaxed, while at the same time grab their attention. Learning a language, combined with music, helps bring students to their fullest cognitive level within a very short amount of time, and as a result, has their brains warmed up for the remainder of the lesson. Various musical activities can be employed within the walls of a classroom, regardless of the age of the students. The easiest is to simply play a song and give the students the lyrics so that they can follow along. This can be a very effective comprehensive activity. Generally, most teachers use popular music that is appealing to a wider audience. Pop songs generally have quite simple lyrics and are not too long, perhaps two-three minutes. Additionally, within these songs there are repetitions, such as the chorus, that help students hear the same material more than once. Also, pop music is very pattern-like, often with a catchy melody which further helps students remember the material. Music to make things more challenging Other types of music may be employed for a more interesting and challenging activity. An example could be to use a more event-guard, or obscure style of music, such as Pia Rolunare by Arnold Schoenberg, in which the music is sung in what most people consider to be a rather bizarre manner. This creates an interesting challenge for the students, as they will have to more intensely focus on what the singer is trying to communicate. This method can be used for all ages and levels of students, however the Pia Rolunare example is best employed with more advanced students. Music activities using instruments As many students may be uncomfortable singing, group activities can also be devised using instruments. I have found it is best to use percussion-style instruments which merely require pulse to play, or a very simplistic pitched instrument which can be taught and understood almost immediately. Alternately, a simple clap along can work as well. As this type of activity is rhythm-based, it can be used for helping learn the pronunciation of syllables, and also the rhythm and phrasing of a language. This kind of activity is particularly useful as it can be used for all ages and levels of students. It is also what I would call a full engagement activity, meaning that it requires students to use multiple functions of their brain, thereby gaining and retaining their full attention. Are you ready to teach English using music? Learning a new language can be a difficult and frustrating process, but by adding some light, fun activities we can go a long way to helping students feel comfortable and relaxed. Speak in the classroom can prove to be a beneficial activity that not only helps relax students, but also engages them to be able to learn in a more effective and focused manner. It is a fantastic warm-up activity to not only motivate students, but also to jump start their brain so they can remain immersed for the duration of the lesson. Speak with an ITTT advisor today to put together your personal plan for teaching English abroad. Send us an email or call us toll-free at 1-800-490-0531 to speak with an ITTT advisor today.


So, in the previous lecture we introduced compactness and we saw that the interval 0, 1 the closed interval 0, 1 is compact. So, just as in the case of connectedness we can ask what happens for products or subspaces. So, if x is compact what is compactness behave with taking products or taking subspaces. So, exactly as in the connected case. So, if x is connected and y is a subspace then y need not be connected. For instance we can take x equal to r and y we can test take this 2 points 0 and 1. So, clearly y is just the union of these 2 points. So, clearly y is not connected and in the same way. So, if x is compact y contain in x is a subspace then y need not be compact. So, we can take x equal to 0, 1 and y equal to the open interval 0, 1. So, there is a homomorphism from r to 0, 1 right and we saw that r is not compact. Thus the open interval 0, 1 since homomorphism obviously is going to preserve compactness. So, and we saw that r is not compact. We explicitly wrote down an open cover which does not have a finite sub cover. What this homomorphism is is left as an exercise ok. So, let us come to products and that is in the as in connectedness if x and y are connected to logical spaces we saw that their product is connected. So, in the same way we will prove that if x and y are compact to logical spaces then their product is also compact. So, the crucial ingredient for that we need is this lemma which is called the tube lemma. So, let y be a compact to logical space let x be any to logical space let w contain in x cross y. So, x cross y is obviously always given the product topology be an open set containing x cross y. So, then there is an open set u contain in x such that x is in u and u cross y is containing w. So, let us make a picture of this lemma and explain what it is saying and why it is called the tube lemma. So, this is our x and this is our y, y is compact and here we have this is x cross y and we have this open set w some open set which contains x cross y. Then what this lemma says is there is a small neighborhood u around x. So, is that this entire disk around x cross y is contained inside w it contains this entire tube w contains. So, this region is w and this is u cross y. So, let us see how to prove this lemma. So, given any point y in y there is a basic open set. So, given any point in y in y. So, we have the point x comma y which is in x cross y which is contained inside w and w is open in the product apology which implies that implies there exists open sets u y contained in x and v y contained in y such that this x cross x comma y this is in u y cross p y and this is completely contained inside. So, we are taking any point over here this point is x comma y. So, we are just saying that this is open neighborhood. So, this is u y this is v y. So, u y cross v y is contained. So, clearly and this happens for every y. So, thus we can write y as a union of y in y v sub y. So, since y is compact this has a finite sub color. So, we can write y as j equal to 1 to n v y j we can write this as a finite union. So, let u be equal to intersection of the u y j's. So, note that each of these u y j's it contains x right. So, therefore, u contains x each of these u y j's is a open set containing x we are taking a finite intersection. So, therefore, u is an open set such that an open set of x an open set in x the point x. So, then u cross v y i is contained in u y i cross v y i which is contained in w and this happens for all i. So, this implies that union i equal to 1 to n u cross v y i is contained in w, but this union is simply u cross union i equal to 1 to n v y i this is contained in w, but the union of the v i i is a simply y. So, this completes the procedure. So, using this lemma which is the crucial ingredient let us prove the theorem on x theorem let x compact to logical spaces then the product x times y is compact. So, let us prove this suppose we are given an open cover. So, then fix an x. So, then we have x cross y which is contained in x cross y. So, as x cross y. So, note that consider the map consider the map y to x cross y which sends y to x comma y right. So, this map is bijection factors through x cross y and this has this subspace to project. So, it is easy to check. So, the map from y to x cross y is obviously continuous because the image of y.  So, this shows x cross y is and now. So, we can write x cross y is equal to union i and i intersected w i right and since x cross y is compact this implies that this has a finite sub cover which implies that this x cross y is actually contained in some finite set w i j. So, by the previous lemma.  So, we. So, x cross y is contained in some finite sub cover we just collect the indices in that sub cover and put it into the set i sub x yeah. So, here is a finite sub. So, now by the previous lemma there is an open neighborhood u sub x of x in x such that. So, what are the previous lemma say? So, let us look at the previous lemma. So, y is compact and if x cross y is contained in w then there is a small neighborhood u of x such that u cross y is also contained in w. So, we will use that u sub x cross y is contained in union. Now, this can be done for every x. So, thus when we do this we get an open cover u sub x. Now, again as x is compact this has a finite sub cover. So, we can write x as u x sub j yeah. So, then x is equal to I am sorry x cross y u sub x x j cross y which is contained in j is from 1 to n each of these is contained in this indexing set w i right and now the index set is finite yeah. So, each as each i sub x j is a finite set subset of i this implies. So, let me just this is equal to union i in this index set is finite. So, thus x cross y. So, thus we have found a finite sub cover right. So, this sub cover is finite because this index set over here that is a finite index set. So, this completes the proof of this here. So, as a corollary of this we see that the closed interval 0 1 I mean when we take product of it n times is compact. So, next let us make some observations about compactness. So, proposition a closed subspace of a compact space. So, let us prove this. So, let y contain in x be closed and suppose. So, our aim is to show that y is compact. So, what we have to show is given any open cover for y it has a finite sub cover. So, given any open cover for y we will construct an open cover for x and from that we will deduce that y is compact. So, let y be equal to union i in i w i b and open cover for y right. So, since y has a subspace topology. So, thus there exists u i containing x open such that each w i is equal to y intersection u i right. So, this implies that y is contained in u i y is contained in this collection of open sets this open in x. So, suppose this is our x and let us say this is our y. So, first we are given an open cover for y this we extend to an open cover for x I am sorry we cover this like this. We find open subsets we find a collection of open subsets in x such that the union contains y right and now since y is closed we may write closed in x we have x minus y is open x right. So, this region is open. So, we can write we may write x as x minus y disjoint union y this containing x minus y union. So, this is open in x and each of these is open in x right. So, x is contained in this and all these are of course contained in x. So, this implies that we have gotten an open cover for x. So, since x is compact this has a finite sub cover. So, let us say the finite sub cover looks like this I mean this may or may not be present, but there is no harm in throwing it in throwing an extra open subset into it. So, now intersecting both sides with y we get y is equal to this is disjoint this empty y intersected with x minus y is empty we simply get this equal to w i j. So, thus the open cover we started with has a finite sub cover. So, this proves that. So, we will end this lecture here and in the next lecture we shall show that a closed subspace of R n is compact even only if it is closing down.