All right, this morning Ephesians chapter two, before we read, I wanna just introduce this brand new series that we're launching the year with that we're entitling saints and sinners. And I want you to know that I have been waiting to teach this series for the last couple of months. One of the things that I've done for the last 20 years as the pastor of radiant churches, every year in the fall, I try and spend some time really listening closely to what God would have me to plan in the next year, as far as teaching and series and what does he wanna say to us as the church? And really tuning in, oftentimes I'll have people that will come up to me in the front or meet me out in the lobby and they'll say to me, you know, pastor, you should really teach a message on this or you know, I'd love to hear you teach on this, it'd be a great, I'd love to have a series on this or that and my answer to them is always, well, that's a great idea, you should talk to my boss about that. Because my number one responsibility is, as a pastor, is to teach what God, who is the over shepherd of this church, is saying to the church. He speaks to me, he emphasizes topics or themes to me and then that's what I teach. There are a lot of things I would love to teach that I have not yet felt led to teach on. Things that I'm chomping at the bit to get to, but I try and really zoom in on what God is saying to us and I will tell you that over the course of the last several months, the theme that I have felt, God put his hands all over is the issue of identity. In fact, so much so that I really felt the Holy Spirit speak to me that 2018 is the year of identity. It's the year of identity and I think that there's something even broader than just us as the church, radiant church in Kalamazoo, Michigan. I think it is a global crisis and issue, but it's also a global word that God is speaking to his people because it's so important. Right now, if you look across the spectrum of the planet, what you'll find is that our world is in a full blown identity crisis. It's in a full blown identity crisis. It's over things of national identity. It's over things, globalism, tribalism, even in our American culture, identity is a major issue. The sense of where do I fit in? Where do I belong? Who am I? Who do I wanna be? Who do people expect me to be? I just see it on, it's always been an issue. The issue of identity has always been an issue, but it's like an issue that's on steroids right now. And I think one of the things that has taken the issue of identity and identity crisis to a whole nother level is the introduction over the last decade or so of social media. Now, I'm not an anti-social media guy. I like social media. I'm like everybody else. I find myself scrolling through it, looking at it all the time, whether it's Instagram, Twitter, Facebook. Sometimes it makes me angry. Sometimes it makes me happy. Sometimes I don't even know what I'm looking at. I'm just doing it. Has anybody else ever been there before you? Find yourself like after an hour, scrolling through and it's like, what did I just see? And what sociologists and psychologists right now are figuring out though is that with the introduction of technology and social media where we're connected to everything and our global neighborhood has become shrunk down to where we're connected to people all over the globe, is that it's actually rewiring the human brain. The way that we think is being impacted by technology. And it's not just changing the physiology of the human brain. It's actually changing the emotional makeup of people because of what we're seeing on steroids. It used to be, when we talk about looking at a screen, it used to be television. And when I grew up, television had three channels on it. And you watched whatever was on one of those three channels. There was no pay-per-view. There was no DVD. Back in the day they had, I think, VHS tapes when they first came out. It was like a big deal. And so we had VCRs and three channels and a VCR. And then when cable came out, that changed everything. It was like 30 channels. Whoa. Now we've got YouTube, we've got Hulu, you've got online, on-demand, 400 channels on cable, satellite and all kinds of other stuff on top of Instagram, on top of Facebook, on top of Twitter and everything else. So here's what happens. We live our lives constantly viewing other people's highlight reels. What do I mean by that? Well, if you've ever watched sports shows or you watch the news at the end of it, they show you, they don't show you the whole game, they show you the best parts of the game. Well, that's what social media is. Social media is our highlight reels. We look at everybody's, oh, today, I'm just eating a kale salad with tuna and these really wild paw paw fruits that I found in some organic shop there. And we think that's how people eat. That ain't how they eat. That's how they portray themselves eating. When they're not on Instagram, they're eating pot pies. We all know it.  And that's like his best look today. What you don't see is when they wake up in the morning, they have to assemble themselves like a Mr. Potato Head to look that good. It's like put this and that and just get the right lighting and airbrush and 24 different filters. We're seeing people's highlight reels but what it's creating is a culture of exaggerated comparison where it causes us to look at our own lives and go, who am I? Who's following me? How do I compare? Do I fit in? How many likes did I get? Did somebody give me some negative feedback? We have immediate feedback on who we are and what we're doing and what it's creating in our culture, social media is becoming like riverbanks where instead of the current carving out the standards, the pressure of culture and popular opinion is determining how we live our lives. Why? Because one of the greatest needs, you might remember this from high school, Maslow's hierarchy of needs is the need to belong and to fit in. And so in a world where everybody's looking, we're taking consensus polls, we're getting voted on every single day and elected to whatever identity we think we're supposed to have in order to fit in and it doesn't automatically guarantee you're going to be the genuine you that you're supposed to be. It doesn't guarantee that you're going to be happy and full of joy and peace. It doesn't guarantee that you're going to fulfill the purpose that you were put here on this planet because if you live your life constantly viewing other people's highlight reels, you are going to be disturbed, depressed and discouraged about your own reality. Identity is not temporal. Identity has to be deeper than what's on the outside. It has to come from a source that doesn't change a source that is higher than I, a source that can speak in from before my past and after my future. It has to come from someone who knows more than just what I look like on the outside. It has to come from someone who is intricately aware and informed about every molecule of my being and the purpose for that being. And there's only one being in the universe that can do those things. And that is the one who created us. He's the only one. God is the only one who has the right to tell us who we are. He's the only one that at the end of our life we stand before and get voted on. He's gonna look at us and he's gonna either say, well done, good and faithful servant or he's gonna say, well, I mean at the end of our lives I don't know how heaven's gonna work but I think on one screen we're gonna see this is the life that you lived and then maybe on another screen God's gonna say here's the one I wanted you to. And it's not an issue of salvation by good works it's just the fact that God does have good works prepared for us to live in them. And that's why the issue of identity is so vital and it is so important because right now let's just admit it church. There are all kinds of voices, all kinds of surrounding circumstances even our own experiences, our fears, our insecurities that are shaping how we see ourselves. Shaping who we think we are. Shaping who we think we're supposed to be. But there's only one voice that we really need and it's the voice of the Lord. And so saints and sinners for the next several weeks we're gonna be diving into the identity issue. We're gonna be talking about how does God view identity? And what I wanna do is I wanna start this year off right. I want you to look with me to Ephesians chapter two and we're gonna read an entire chapter of the Bible together. Isn't that amazing? A whole chapter. Some of you are like I need to get back on reading the Bible through. Well, today you're gonna be able to check the box. I read a whole chapter of the Bible and I did it with a thousand of my closest friends. Here we go, you ready? Ephesians chapter two, I'm gonna read it, you follow along. It says, And you, he made alive who were dead in trespasses and sins in which you once walked according to the course of this world, according to the prince of the power of the air, the spirit who now works in the sons of disobedience among whom also we all once conducted ourselves in the lust of the flesh, fulfilling the desires of our flesh and of the mind and were by nature children of wrath, just as the others, but God who is rich in mercy because of his great love with which he loved us, even when we were dead in our trespasses, he made us alive together with Christ by grace you have been saved and he raised us up together and made us to sit together in heavenly places in Christ Jesus that in the ages to come, he might show the exceeding riches of his grace in his kindness towards us in Christ Jesus for by grace you have been saved through faith and that not of yourself, it is the gift of God, not of works lest anyone should boast for we are his workmanship created in Christ Jesus for good works which God prepared beforehand that we should walk in them. Verse 11, therefore remember that you once Gentiles in the flesh who are called uncircumcision by what is called the circumcision made by flesh by the hands that at that time you were without Christ being aliens from the commonwealth of Israel and strangers from the covenants of promise having no hope and without God in this world but now in Christ Jesus you once who were far off have been brought near by the blood of Christ for he himself is our peace who has made both one and broken down the middle wall of separation having abolished in his flesh the enmity or hostility that is the law of commandments contained in the ordinances so as to create in himself a new man from the two thus making peace and that he might reconcile them both to God and one body through the cross thereby putting to death the enmity and hostility and he came and he preached peace to those who are far off to those who were near and brought those who were far off near for through him we both have access by one spirit to the father. Verse number 19, now listen to this it says now therefore you are no longer strangers and foreigners but fellow citizens with the saints and members of the household of God having been built on the foundation of the apostles and prophets Jesus Christ himself being the chief cornerstone 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. What an amazing chapter. Chapter two just like really if you look at it chapter one, chapter two and chapter three in the book of Ephesians are all about identity. You see here's what I know is the enemy works best in environments of confusion but God always does his best work in environments of clarity, wisdom, light, truth. When truth is spoken there's clarity and there can be order. First Corinthians chapter 14 says that God is not the author of confusion. It says in James chapter three about confusion it says where there's envy, where there's self seeking that exists confusion and every evil thing will be there. See identity when we're trying to find our identity out of selfish ambitions or out of just our feelings or our emotions when we're trying to define who we are by our drive and our ambitions it says it creates an environment of confusion and confusion is like throwing chum in the water for sharks. When there's confusion in your life the enemy can smell confusion just like you can smell fear and he comes running to environments of confusion because when there's confusion he can begin to twist distort things and bring about his ultimate goal which is to destroy, to kill and to steal but in an environment where there's clarity where there's truth things can be put in order and the enemy is expelled from environments of clarity and wisdom because he can't stand truth. He's repelled by truth and truth brings life, confusion brings death. Why is that important? Because we need to realize today in our culture the voice that is the loudest on the issue of identity is the enemy's voice and he's doing everything in his power to confuse people in their identities. It doesn't matter whether it's racial divides, national divides, sexual orientation all of these issues right now are identity issues. I've never ever seen the level of confusion in a generation like I've seen in the generation that we're living in and let me tell you that that's not by accident and it's not by evolution. It's the result of a demonic strategy to steal an entire generation from their inheritance from their purpose because someone can't live out of purpose that's not connected to an identity.  If you just think you're an animal that you are driven by your basic instincts you'll live your life in a certain way. If you think that when you were created it was a mistake you'll live your life in a certain way. It creates fear, it creates insecurity and instability, it's confusion. But here's the good news is God from the outside is not looking at us irritated, frustrated, mad and full of anger God's answer to our identity issues is he sent Jesus. God's answer to our identity issues is he didn't shout to us from the other side of a curtain where he's in eternity in the spiritual realm and we're living in our everyday life and say get it right guys. No, what God did was he said in order for you to understand your identity you have to understand my identity.  You were created to bear and reflect the image of God. Well how can you reflect what you don't see? So when we see Jesus we see God God came and expressed the image of God so that you and I can walk into that same identity. You see the reality is the enemy tries to confuse everything but from heaven's perspective identity is really binary it's just one or the other. God doesn't look and see oh black and white. He doesn't ignore black and white he's created diversity and it's beautiful but that's not how he divides identity in our world. He doesn't see young and old he doesn't see American and whatever he doesn't see Republican and Democrat he doesn't see gay and straight he doesn't see any of these things that we try to use to define who we are what God sees is lost and found he sees saved and dead living and dead or what we're gonna define as saints and sinners that's how God that's the binary identity issue that from heaven's perspective he looks at because one a sinner has one nature and a saint has one nature I know that in some spiritual communities and some traditions saint is reserved for like a handful of people who perform miracles and lived you know just like a mother Teresa type of a life and we call those a saint but can I tell you that's not what the scripture teaches the scripture over and over and over refers to the saints it's talking about to the saints who are at Colossae the saints and Ephesians 118 it says the inheritance that we have in the saints it says right here in verse number 19 that we are no longer foreigners and strangers but we are fellow citizens with the saints he calls us saints so those who are in Christ Jesus those who have heard the gospel those who have believed in Jesus Christ something happens on the inside of you that shifts and changes your identity where you go from being a sinner to becoming a saint and a saint means one who has been changed, saved and redeemed and changed in our internal nature and a sinner is one that we just read about in Ephesians chapter two that this is how we used to be we used to be driven walked according to the course of this world we used to be under the influence of dark spiritual influence we were the sons of disobedience we by nature were children of wrath which means who deserved wrath God's judgment we deserve that it wasn't just our behavior it was our nature identity comes down to the core nature of who we are it's not just our behavior it's interesting to me that when you see people who do really bad things and by the really bad I mean worse than we did is you'll always hear people say well they're really a good person they have a good heart well can I just burst your bubble for a second no they don't because out of the abundance of the heart our words flow our actions flow so whatever our actions are it reveals what our heart is we do really bad things because we have really bad hearts and in a world, listen I know we're Americans and we live in the self-help aisle I know that we live in America and it's like chicken soup for the soul you're a champion and everything's good and you're just dog on it you're a good person no you're rotten in your humanity to the core of who you are you are a sinner broken dead you're a zombie like the walking dead you're living but you're not really living you're you hear a noise you're not alive none of us are spiritually we're zombies we hear a noise we're driven by appetites that's where God finds us but praise God that when God sees us like that he doesn't leave us like that he sent Jesus to change us you see the reality is your identity is not defined by your temptations your identity is not defined by your failures you are defined by what you do with the gospel that's who you are sinners by nature how many know when you have a little baby they come out really cute all of you came out really cute by the way but if you've been a mom or dad or an older brother or sister little babies come out and they're just precious and everybody's just like oh look out they're so sweet oh they're so innocent they're just they are they're beautiful but by one two years old when they begin to learn to talk how many know what their first words typically are I know mama daddy all that but then it goes no it's like who taught you that word no little the brother tries to take some you know play with a toy no or how about this one mine all of a sudden your cute little baby turns into gollum it's like depresses he's trying to steal the promise depresses just the hobbits meee it's like where did you come from all of a sudden there meee what happened to my cute little two year old have you ever noticed you don't have to train a child to say no you don't have to train a child to share I mean when's the last time you saw a parent goes no you're sharing too much you're too nice you say yes to everybody I need to teach you to open up say no pull it closer hold it where does it come from it comes from the nature that we're born in the Bible says we're born into Adam as sinners I know that nobody wants to be told you're a sinner but listen you can't be cured of a disease that you've never been diagnosed with and if we're just trying to become better versions of ourselves clean up our external we're never going to change our identity at the core and that's what Jesus came to do not just make us better versions of ourselves not just decorate us in a better way not to just make us more photogenic for our social media platforms he came to resurrect us from our spiritual death forgive our sins which we could never reconcile ourselves and translate us out of darkness and death and blindness and bring us into the kingdom of light he came listen Jesus came to take slaves and make them kings and queens he came to make orphans children of God he came to make blind men those who are prophetic he came to take those who are dead and in the tombs and resurrect them from the dirt that's what the gospel of Jesus Christ is all about and yet we allow so many of the things of our past to define us and even in the body of Christ we have some just terrible ideas about our identity okay so this is what a sinner is a sinner here's what sinners do a sinner ready sins it just comes natural but a saint somebody who it's not just a sinner who's rehabbed but it's a new creation 2 Corinthians chapter 5 verse 17 says if any man or woman is in Christ Jesus they are a new creation all things have passed away and behold all things have been made new a new a brand new creation in Christ Jesus and here's where we get bad theology a lot of times we know what sinners do we can nail that down pretty good at our lowest most humble moments when we know we need God that's when we say I'm a sinner but then what happens is we come into the church and here's what this series is really going to be about we come into the body of Christ and we still see ourselves as sinners just forgiven sinners some terrible bumper stickers out there I'm just an old sinner saved by grace that's really cute but it's bad because Jesus didn't come to make sinners better Jesus came to make dead people alive Jesus didn't come to give you a divine magic marker eraser that every time you sin it's like oh the blood of Jesus I just raised my sin okay but it's still me and I'm just I'm gonna sin I'm an old sinner oh every time I mess up God's grace is sufficient I'm so grateful for God's grace I'm so grateful for forgiveness of sins I'm so grateful that when we confess our sins and we plead the blood of Jesus he faithful and just to forgive us our sins but can I just tell you you're not just an old sinner saved by grace if you're saved by grace then something more at a nature level spiritual level has happened on the inside of you you've changed you've been born again of the spirit of God you've confessed your sin you are a sinner and you've confessed that what Jesus did on the cross is stronger than anything you've done in your life and you let his grace come and totally change you from the inside out and now spiritually you might have the same look live in the same house drive the same car have the same friends but you've got a new name and a new identity and you've got a new nature on the inside of you and we gotta get a hold of this new nature because as long as we see ourselves as something less than a saint I'm not talking about you're never gonna make a mistake again I'm not talking about you're not even gonna sin again I'm talking about the core of who you are has changed and it will grow and develop and become more like Christ that's the goal that's the goal that God has is that your salvation point is the starting point and throughout all the days of your life he's going to begin to change and shift you to be more like Jesus there was this story that was run in the UK about a homeless man who knew that he was a millionaire he was found dead before it could be told to him this is from 2010 it says a long lost relative of the reclusive and eccentric New York hewgett clark who stood to inherit 19 million of her 300 million dollar fortune has finally been found unfortunately dead from hypothermia in rural Wyoming Timothy Henry Gray's body was discovered by children sledding under a Union Pacific railroad overpass in Evanston Wyoming in the southwest part of the state temperatures had hit 10 degrees below zero gray who was 60 was the half great nephew of Clark who died in May 2011 age 104 and tragically was unaware that he was potentially entitled to 6.25 percent of her copper mining fortune which if you break it down is equivalent to about 20 million dollars and so they had and you read the rest of the article they had enlisted private investigators and attorneys for several years to track down her last living relative they knew who he was so they just couldn't find him because he was living homeless and when they finally found him actually kids found him because they found a frozen corpse of a 60 year old homeless man I wanted to think about why was he homeless and why was he dead well because he probably didn't think that he had money to buy a house or a car or warm clothes or food on paper he's worth 20 million dollars but it's only the money you know you have that you can spend so technically he's a millionaire functionally he was a pauper it says my people perish for their lack of knowledge in other words what you don't know can hurt you and there are a lot of us who don't know that beyond just our sins being forgiven you have a new identity in a new name in Jesus Christ in Christ Jesus when you read Ephesians chapter 1 what you quickly realize is it's all about Christ it's all about what he has done it's from the very beginning it says that you and I in Christ in the Lord Jesus Christ have been accepted in the beloved he chose us in him that we're made holy in him that he's expressed his love in him that we have redemption through his blood in him that we've received the riches of his grace that we are seated with Christ in heavenly places that we've been given a new name I mean in him in Christ Jesus everything has changed about our identity everything has changed you may think your name is Bob Smith and you live in Kalamazoo, Michigan and you're a middle class and you've got a job and you're dreaming about retirement and you've got this home and you've got your family and you've got your struggles and you may think that that's your identity but let me just tell you there's a higher identity for you Bob Smith you may have that name here on the earth but he has another name for you you actually have a throne in heaven in which you are seated you have authority over demons you have authority over hell you have authority over sin you have the spirit of the living God that called the planets into existence dwelling on the inside of you you have royal blood flowing through your veins your name is written in a book by the hand of God you have your name written on the palms of Jesus' hand he knows you when you pray he hears you the inheritance that belongs to you the Bible calls you an ambassador of Christ you are literally a missionary from heaven that was sent to this earth and although you might not know your purpose before you ever took your first breath God knew your name and had a plan and had a purpose for you that he sent you to earth to fulfill that did just shock us your name might be Stacy Smith and you think well I'm just mom raising up kids no you are an ambassador from the kingdom of God you have the signet ring of your father on your finger all authority that Jesus had belongs to you you will live forever you will never die God's word is your inheritance everything that he writes in here belongs to you there is no demon in hell that can stand in front of you because of who you belong to when the devil sees you he sees Jesus we can't live homeless I don't want any of us Christians to be found at the end of our lives spiritually as if we are living under an overpass let me just let me illustrate it to you this way I am running along these guys are gracious lovely worship team see here is what typically happens the enemy convinces us that we are defined by the dirt of our life that's who you are that's the devil's dirty little secret this is who you are see if you understand what dirt is dirt is decayed organic matter decomposed at one time dirt was something that was alive it was plants animals it was matter it was wood it was trees it was flowers it was fruit it was an animal it was a person but through death and decay it breaks down what we are left with is dirt this is how the enemy thinks he's got dirt on us what he says to you is you want to know who you are and he holds up the hand a handful of the dirt of your life and he says this is who you are the things that were alive in your life your marriage that you went into all of a sudden one day it began to break down and you were served with divorce papers and now you live with the stigma of being divorced all the days of your life it's something that was alive that broke down and is now decomposed it's the dirt of your life and the enemy will hold it up and say this is who you are this is how you are defined some young person some young seven year old boy goes into his dad's bedroom and finds hidden under his bed a magazine filled with pictures and images that no seven year old boy is designed or equipped to handle and he sees it and stirs feelings things on the inside of him that for the rest of his life he's going to struggle with and it becomes lust and lust becomes a habit and it becomes guilt and full of shame on the inside of him and it constantly draws him back it promises him pleasure but all it leaves him with is nothing but decay and dirt and the devil then piles on the guilt and shame on us and says this is your identity it's your failings some little girl sexually abused at the hands of somebody older and for the rest of her life she feels as if her innocence has been lost and I'll never be able to get it back I'm abused and that becomes an identity a man begins to drink a little bit too much and pretty soon becomes dependent on and he goes to the bar and hangs out with his friends and he gets in the car a little bit too drunk he gets pulled over by a police officer because what belonged in high school to just a can of beer with his friends has grown into an addiction that now has cost him his driver's license and then costs him his marriage and then cost him his job and now has cost him his dignity and the devil promises you life but all you're left with is dirt and then you hear his voice say this is who you are and on and on it goes the drugs, the lust the sex the impulses the things that are nothing more than the dirt of this earth what it says in Ephesians 2 is the pattern of this world this world is dust, it's dirt and the Bible says that even our physical body is dust to dust dirt to dirt we shall return but can I tell you dirt is not your identity this is not who you are see because one day at the very beginning of time God the Father walked in the garden of his newly created earth and he looked at the mountains that he said are good and he watched the birds fly across the sky and he said it is good he looked down into the water and he see the schools of fish and he said it's good the grass in the fields and he said it's good and then God knelt down into his new earth and he took up a handful of dirt and it says and out of that dirt he formed man and it says and when God breathed the breath of life into the dirt it became a living being let me tell you what God has an amazing ability to do to reach into the dirt of our lives things that have defined us branded us we've allowed to become our identity if we will allow it, God by his grace here's what grace does grace reaches into the dirt of our lives and he shapes a masterpiece in the image of his son Jesus and then by the power of his Holy Spirit he breathes life his life into our souls we become a new living being a new creation Ephesians 2 verse 10 says we are his workmanship Jeremiah 18 says I went down to the Potter's house and the Potter was sitting at the wheel he had clay on the wheel and he was making something new he was taking the broken pieces and he was making something new only God is able to reach and say the dirt is not your identity the dirt is just the building block materials by which I'm going to form my masterpiece and I'm going to cap it all off just like you did in the very beginning and I'm going to breathe my life into you I'm not going to just leave you to try and figure it out on your own if you'll let me my grace will shape you and my spirit will fill you with my new life and you can go from being a sinner that's defined by your dirt to becoming a saint that is defined by the artist you see God is in the habit of taking the filth of our life and making something beautiful out of it Jesus has this encounter with Simon Peter in Matthew 16 and he says to Peter says Peter who do people say that I am well some say you're John the Baptist some say that you're Isaiah the prophet some others say that you're Jeremiah one of the other prophets and Jesus then responded to him and said this who do you say that I am who do you say that I am well you're the son of the living God listen to what Jesus his response was he says blessed are you Simon Bar Jonah for flesh and blood has not revealed this to you but my father who is in heaven and he says this and I say to you you are Peter and on this rock I will build my church what happened Simon heard God tell him who he was after he had a revelation of who Jesus was our identity is found when we come face to face and acknowledge his identity you are more than a good man you are the son of God you are more than just a God who is in the farthest corners of the universe you are the son of the living God savior of the world Jesus you are not just a figment of my imagination you are a perfect man fully God who died on the cross and you bore my sins penalty you were raised from the dead alive and you reign in rule you are king of the universe and I am not the king of the universe I got all the pieces but I don't know how to put it together when you acknowledge who Jesus is he steps in and he puts the hands of grace to the dirt of your life and he says now let me shape you and tell you who you are and only God has the ability or the right to tell you to shape you into who you are always meant to be because only he knows what his plans have always been for you and it doesn't matter what you've done where you've been he's able to take any sinner and turn them into a saint because his grace is sufficient would you stand up with me all over this room there's an inheritance that belongs to every child of God the key to you walking in your destiny is letting him define your identity show you your inheritance next several weeks we're going to be digging in what does it mean to be a saint what does it mean to be a follower a new creation a Christian I know what our culture says it means but I don't care what culture says I care what God says and I think many of us in this room are going to discover that the person you thought you were pales in comparison to who you really are who he's made you to be in Christ Jesus would you bow your heads with me all across this room please this is a sacred moment you see the same father who stepped into the garden in Genesis chapter 2 is the same father who stepped into this service this morning and he came with one intention as a father to leave this room with more children than he came with you may be here today and you say you know Pastor Lee as you were describing a sinner that's who I am you were talking about the dirt I've got so much dirt can I tell you I am not here in any way Jesus did not come and I'm not here to condemn in any way I'm here to announce good news doesn't matter how much dirt you got in your life doesn't matter how many times you've sinned how broken you are doesn't matter how far you've gone today Jesus will save you he will forgive you he will rescue you and he won't just brush you off and tell you to do better next time today if you'll put your faith in your trust in who he is and what he did on the cross today you can be born again you can be changed from the inside out you can become a child of God lay down your sins lay down your striving lay down yourself and let him resurrect you from the dirt all over this room I'm asking you to respond to what the Holy Spirit is prompting you in your heart today you know whether you're right with God or you're not today many of us in this room need to get our lives right with God and the Bible says if we here's how we receive the grace of God we don't do anything we just open our hearts up and say I believe if anyone will call upon the name of the Lord they shall be saved all over this room I know right now the Holy Spirit is already doing his work you know in your heart of hearts you're not right with God you know you're a sinner today you know you need the forgiveness of God the real life-transforming forgiveness of God in your life today I'm going to ask you to respond in faith to it I'm going to ask you to take a step and say I want a new identity I want to be found a saint in Jesus I want to be forgiven I want to know I'm right with God pastorally pray for me and we're going to pray together in a moment I want you to respond right now just raise your hand say that's me I need to get my life right with God in Jesus thank you all over the room come on just raise it this is not something to be ashamed of this is exciting this is good this is a birthday hands all over the room yes yes yes yes yes yes all the way in the back row see your hands this is awesome you can put your hands down thank you so much everybody here's what we're going to do we're going to pray this together this is a confession this is us talking to God and we're going to do it together say this with me say heavenly father come in Jesus name and I believe Jesus is the son of God the savior of the world I believe he died on the cross to pay for my sins penalty so that I could be free I believe he rose again from the dead and is alive forever I confess I've sinned I've lived for myself I'm a sinner today make me a saint come into my heart be my lord be my savior wash me clean give me a brand new heart from this day forward I'm a new creation I'm not who I used to be I'm a child of God I have a future I have a family and I have a father I will never be the same again in Jesus name amen if you just prayed that prayer welcome to the family of God we are so proud so excited for you so good so good we're so proud of you so awesome man it never gets old seeing people go from death into life amen church I mean it's just man it's just so good listen here's here's how we want to dismiss this morning I'm going to invite our prayer our ministry our care team members pastors if they would come make their way down to the front those of you who just raised your hand and you just prayed that prayer everything has changed but let me tell you you're going to need help walking it out we all need help and we want to invite you to do take your next step and here's what your next step is you need to tell somebody and so when everybody is leaving this morning those of you many of you you're not alone I promise you raised your hands prayed that prayer and meant it truly meant that I'm going to ask you when everybody is dismissing for those of you who prayed that prayer and really meant it walk down to the front to one of these prayer partners here and even if you have to wait for a minute and just tell them I just prayed that prayer we want to pray with you we want to give you something a bible if you don't have one we want to give you a book that's going to encourage you we just want to look you in the eye and tell you welcome to the family of God and everybody else we'll see you this Wednesday night for seek at the Portage Campus at 6.30 have a blessed afternoon come down forward if you just received Christ


Hello there everyone and welcome. My name is Melissa Armel and I own the Stock Swoosh and today I wanted to talk to you about shorting. Just go over here to Adobe. This was the Stock Swoosh Show play of the day today. The stock had a big move down on the earnings from last night. It gapped down from last night to this morning and fell off a cliff. This is lower and it had a big red bar. What does that mean selling? So panic came into the stock. One of the reasons that I loved to short and I prefer to short rather than go long is because selling moves happen quick and fast. So panic comes into a stock when the price drops. Just think about it. I mean, it's really common sense. So that is one of the reasons I like to short. This has been a great year for shorting and again, it's so interesting to me how so few people that trade the market actively trade retail traders so few people know how to short or even like to short. But you've got to learn something to do in the market if you want to have a piece of the pie that is a niche. And I've created a niche for myself by not only doing gaps and have a preferred way to do gaps, which I uniquely created by myself, which is my own method, but I also have a niche in the sense that I prefer to short. So I'm an expert in shorting. That has allowed me to also read longs and strength very well because I can see weakness. So I can see when something's weaker when it's not weak. So again, it's been advantageous to know how to short and focus on that first because it's allowed me then to see what real weakness looks like on the one side and that one real what real strength looks like on the other side. So that's how I know also when to go long. So again, while I will go long, I prefer to go short. And I think 2022 is a great year for traders to learn how to short. If you're someone that's trading, if you're actively trading, if you're in the market at least three days a week or more, you should know how to short. If you don't know how to short, you have missed out on a lot of big moves in stocks and the market this year so far just in the last three months, just since the beginning of 2022. There's a big, big part of the year left. Okay? There's nine more months left in the year. Don't miss out on the rest of the calendar year where we can have some beautiful swings to the downside. Everybody on this retail trade is most of them want to buy the dips. I think that's the thing to do. No, no one should be buying the dips right now. That's number one. It doesn't consistently work. It's not a strategy either. That's two and three. And again, if you don't know how to short, you're missing out on huge opportunity to make money in the market and you're getting killed actually many, many days and weeks since the market has sold off for the majority of the year of 2022. And although people see the rally, we've had the rally the last week. I get it. I get it. The fact is, if you don't know how to short, you were going to miss out on the downside move when it comes. It could come today. It could come tomorrow. It could come next week. It's coming again. And again, shorting is something that you have to learn how to do correctly. I had a friend years and years and years ago when I first started trading said, Melissa, I don't understand what you do. It's like you're shorting thin air. Like you're shorting in the middle of no man's land. And that is kind of what we do a lot of the times really. But I have a method that I invented. It took three years of my life to create this method. And it works. And I've been teaching people now for a very long time, you know, 10 years plus. And we got this Adobe today was a great move. It was 100% conviction. We did it. We were in and out fast. But I will tell you again, this is just indicative of what more of what we're going to see into our new season in April. And again, what we're going to see in the market as well. And we'll just look at this here very quickly. We're shelling off here under the close. So market will close red today. Could be a baby red. Could be a medium red. We got 45 minutes left. We'll see. This is going to close red today. Absolutely. And we're probably lower tomorrow. I don't know exactly because again, tomorrow is a long way away from the market, but I would be shocked, shocked if we don't fall again tomorrow. So this is an interesting time. You've got to learn how to short. If you would like to learn how to short, email me at unless at the stockswush.com. I will tell you the classes I offer to learn the next class for the big class that you learn the strategies this weekend, March 26 and 27. I have a few spots left, but the deadlines tomorrow outside of that, you know, you can sign up for the options newsletter and get the short calls that I've been, I've been calling the puts that I've been calling in the newsletter. But it has been a great time to trade here. And we've had perfect entries and just like in this Adobe this morning show really excited about the future, really excited about 2022. But if you are someone that's trading and you don't know how to short, you've got to learn how to do it and don't do it if you don't know how to do it because you can get hurt. You always have to learn what to do before risking your own money. You don't want to lose. You want to win. So if you want to win, you've got to learn what to do. And again, there's a cost involved with that. You're paying me for my information and my time to learn from me to get mentored to learn. So this was a nice call today. Everybody did great. We'll see where it goes. Email me at melissathestockswish.com if you'd like more information. Have a great day.


Pretty much doing the same thing as far as conceptually. Obviously, when he's in there, he's their guy, he's their number one target, very explosive receiver. Obviously, we've seen him last year. One of the best, not just young, but best receivers in the league, even though he's been in there only a second year. But two Higgins is a guy that's been really stepping up. I always felt like he was a really good receiver, good catch radius, good arms, good arm length as well. But they have a lot of weapons all around the field. Then you got Joe Mix in the backfield as well, and Hayden Hurst is playing really well as well. He trusts him across that middle. Joe Burrow, man, he might not be the guy that always is kind of mentioned with Mahonze or Josh Allen, but he's definitely right up there is one of the best quarterbacks in the league. You kind of mentioned that they do get the running backs involved a lot in the passing game. How much do you guys have to be aware of that? I mean, a lot. Because, I mean, they're a part of that passing game. And obviously, Samajay Piran, they scored three touchdowns last week. It's a stiller. So I know Joe Mix is in concussion protocols. Not sure if he's going to play or not. But if he can't go, Samajay Piran, Samajay, we have to be aware of in the passing game. How much did the rest help? I mean, a lot.  And I think everybody's going to be energized and ready to go this week. So I know fans think of it that way. I mean, now to get them back here, kind of nice to have them here on the road again. I mean, it makes sense for the fans to feel like that. I mean, I'm not saying that we're looking at it is just another game. But I hope that the fans really feel that way because they should come out super amped up. Tailgate, Naud, they'd be excited for this game because we're going to need them, especially on third downs, because they're really good on third. Finally got through though. It was kind of a long process going through it. Treatment took a while. Climbs up back here and there. But to finally get through it, at some point, I was thinking, oh man, my career might be over. God, because it's taken so long. But then finally being here, really grateful and really happy and really excited to go back out there and hit the balls. Were you seriously worried that you wouldn't be able to come back from it? Oh yeah, definitely. That was just a terrible mindset I had at the beginning, just thinking like, man, not feeling better today. I'll set back today.  But at the end of the day, my body was my body and it had to do what it had to do. But yeah, I was definitely got down at points. But yeah, so I was very excited being back and very excited to go out there and hit the balls again. When did it start to kind of feel better and realize you were trending in the right direction? Really started feeling better about the end of camp kind of early in the season. So a little bit late, but you know, that's all I could do was go in and work with the trainers, work with the strength staff and do what I could do. But yeah, just a little late into the year, early in the season, a little late after camp. But yeah, it was just, I was about to start feeling better. And then from there, it's just been like a slow progression to get back to the point where I could, you know, compete and go out there and do my job if needed. So. I feel like I can't get as ever now. Oh, I feel like I feel great. I feel like I've gotten back to the point where I was before and excited to get that, you know the real live work again, try to get that rhythm, get that timing and, you know, get that, just get that practice in. So. It was kind of a freak injury because you hit the ground with your foot, right? Yeah, it was totally unexpected. It was feeling great and nothing lighted up to it. It wasn't thinking, you know, I had no soreness, no pain, nothing. And then yeah, it was just kind of a weird, or an incident, weird incident, so. When that happens, you're an under-affid guy worries that, you know, that they might not want to keep you around to let you get healthy. Definitely, you know, I know with NFL, being a business a little more in college, I was, my first thought was, man, this might be it. Like my career might be over 40 even started. So that was definitely part of, you know, my mindset I had, that beginning was just kind of so worried. I didn't know what was going to happen. So I had a lot of questions, a lot of concerns, but, you know, the organization coaching staff, the trainers were so patient and so helpful that they instilled a lot of confidence in me during that process.  So. Was there any surgery involved or just rest and rehab? Just rest and rehab. Yeah, no surgery involved. Just kind of, you know, let my body do what I need to do. And however long it took, however long it took, you know, it definitely just took longer than I wanted. But yeah, it was, did what I could do. And it was a long process. What happened now, man? Just told you, just get back after your kick and we'll just kind of see what happens from here.  So I know he's going to do what he can to help the team win. So just go out there and give it my best and try to improve every day. So. It's done that on the first hand experience as a player. As a young pass rusher, you know, you come in and you make a sensation, make a few sacks and all. Do you notice that opposing defenses or opposing offenses are now trying to counter what you do and you're having to counter back with them? Is that part of it now? Yeah.  A lot of guys having lots of sacks and it's just, they have been all throughout the league. So I think offenses in general, whether it's me or anyone, they just know pass rushers are on a mission nowadays and they have to be able to stop them to be able to compete and have the offense they want.  Do you try to add to your pass rush repertoire and your moves throughout the course of the season or is that something you work on in the off season? Yeah, I think mainly starts in the off season. But for me personally, I'm a guy in camp, you know, every week or two of camp, I have a set of moves, two of the moves that I try to really focus on to have them in my, you know, in my bag or in my repertoire. And then during the week, based off film, and what you think will work best against those offense attackers, you know, you practice them back in there and camping, you can pull them out and work them all week so they'll be tuned up for the game. And I think that just, obviously always have your go-to moves, but when you have that ability to have moves to switch it up, they think you will be able to work at a high level, it gives you an advantage. What do you think their offense has done, even though Chase has it in the line-up? Obviously Burrow still has a line-up, I think he can choose from, right? Yeah, I mean, if you look at their ranking and stats on the offense, it's an explosive offense and it shows, they put points up and they hit huge X plays, big plays down the field and Joe Burrow likes to sit back there and look for those target Seattle's out on the edge, guys that can really make things happen from Jamar Chase to Boyd, Higgins, all those guys, those are threats all across the field.  We'll be able to do what we need to do.


So, yeah, so last time we talked about group operations, so that, so we have a group G acting on a set X, so this is a map from G times X to X, so G pair of G and X is mapped to something called G times X, which satisfies two actions, namely that if we kind of twice pick these two elements in this way, we compose the action twice, it's the same as if we multiply the elements in the group and act by that, and then the identity element should act as the identity, so this is for all X and all G and H. And we had introduced two important concepts connected with group operations. One is the stabilizer and the other one is the orbit. So the stabilizer of an element will just be the set of all elements in the group which map it to itself. So this is GX, which is the set of all G and G, such that G times X is equal to X, and we also have the orbit which is just all the elements of X, so the orbit of an element X and X will be the set of all elements of X which we can reach by acting by elements of G on it. So this is G of X, which is a set of all G times X is G and G. So this is a subgroup of G and this is a subset of X. And we had seen that if we have a group operation, then we get a decomposition of X into this joint subset, so then the different orbits form a decomposition of X into this joint sets because they are actually equivalence classes of an equivalence relation. And we finished by the orbit stabilizer theorem which said that where we have a group G acting on a set X and we take R, a system of representatives for the orbits. So in other words, this is a set which contains one element out of each orbit and then we find that the number, so I want G X on X, and in this case the X is finite, then the number of elements of X is equal, this is kind of trivial, sum over all these representatives of the number of elements in the orbit of X. This is just the statement that X is the union, the disjoint union of the orbits and we can rewrite this as the sum over all X and R of the index of G in GX because one finds that the number of elements in the orbits is precisely the index of GX in G. So this is actually a very simple result but it's useful and therefore it's a theorem. So now we want to look at the special case of an action, namely the action of a group by itself by conjugation, group G on itself. So first what does it mean, conjugation? So we have G a group and we see that G and H in G are conjugated if there is an element A in, if there exists element A in G such that say H is equal to A G A to the minus 1 and you can easily see that this is an equivalence relation, this is a trivial exercise. And so we can look at the equivalence classes which are called conjugacy classes of elements are called conjugacy classes of G. So we want to say something about these conjugacy classes and we want to see that this actually is an operation of G on itself. So let's first define something more. So for an element X in the group the centralizer of this element consists of all elements commuting with it. So let X in G, so the centralizer of X is just, so I write it with Z of X to be the set of all G and G such that GX is equal to XG. So these are all elements which commute with our given element X. I have some simple remark. First the centralizer of any element X is a subgroup of G. That's very easy. Then I can look at the center in the exercise. I use the different notations C of G but I want it now with a Z. C of G is, we know it's a normal subgroup of G and this will always be a subgroup of the centralizer of any element X. That's obvious by definition. The center consists of all elements in the group which commute with all elements in the group. So in particular that's a subset of all those which commute with a given element X. And it's also obviously a subgroup. And finally we have an element X in G is in the center if its centralizer is the whole of G. Again this is trivial because the elements in the center are the elements in the group which commute with all elements in the group. And that's precisely what's being said here. Okay so this is really a remark. There's nothing to prove. Everything is directly from the definition. So it turns out that the conjugacy classes are somehow very important in variant of the group and if one wants to understand the group one has to understand the conjugacy class. We will not really do that. Maybe in the next semester you will also hear something about representation theory of groups and you find for instance there's a close relation between the representations of the group and the conjugacy classes of the group. But now we want to describe this and we want to describe the conjugacy action of a group on itself so that the conjugacy classes will actually be the orbits of the definition. So the conjugation or action of G on itself is just the obvious thing. This just is defined by G times H is equal to say G H G to the minus 1. Okay so the element G acts on the element H by this conjugation. So by definition the orbits are precisely the conjugacy classes. These equivalence classes are precisely the conjugacy classes. So the conjugacy class of an element G is the same as the orbit because you know after all this is precisely how it was defined. And we note also that the stabilizer of an element say X in G with respect to this conjugation action is precisely the centralize of X. No, because by definition the centralizer of X is equal to the set of all G and G such that G X G to the minus 1 is equal to X and this is obviously equal by multiplying by both sides by G and multiplying on this side by G to the set of all G and G such that G X is equal to X G which is and so now I said it precisely wrong so this is the stabilizer is by definition this and this is the centralizer of X. So this statement is also obvious. So now we just basically we just want to reformulate the orbit stabilizer theorem for this conjugation action and then it gets a new name. It's called the class equation. So it's just another way to count in some sense the elements in the group but it's actually just a special case of the orbit stabilizer theorem but still it's a useful result therefore it gets its own name so theorem class equation. So we take G a final group and so we take R to be a set to a subset of G which contains precisely one element from every controversy class so such that every element in G model of the centralizer of minus the centralizer of G every element in G which does not lie in the center of G is conjugated to precisely one element in R okay then the number of elements in G is equal to the number of elements in the center of G plus the sum over all elements in R of the index of the centralizer of X in G. So in some sense note that in some sense I have here it's formulated in some sense in an unnecessarily complicated way as we will see in a moment but this is usually the way one wants to use it so that's why we write it like this. So note we can say it also as follows so maybe I can prove it and prove it and then we can see. So we take a system of representatives of the orbits of the conjugation action of G on itself then maybe then we can apply the orbit stabilizer theorem in that says that so by the orbit stabilizer theorem we have that the number of elements in G is the sum of all X in R of the index so of R prime was our system of representatives the index of the stabilizer with respect to the conjugation action of this X in G and we remember that we had just seen that this stabilizer was actually the centralizer of X so we get this formula still with the prime and now we have to we see that if our element X lies in the center of G then it commutes with all other elements so its centralizer is the whole of G so this index is equal to 1 and so we put just so it means that on other words we also have that if it lies in the center of G then it's also clear that the orbit G of X is just equal to X because after all by conjugation because it commutes with every element G in G so if I make G X G to the minus 1 then this is equal to X so it means that the center so therefore we can put just put minus the center of G so if you have an element in the center then it is automatically equal to its own conjugacy class so in R prime all the elements of the center are represented and we just remove these and in that case if we have an element in the center then this index is equal to 1 because these two are equal and so this formula is just equal to the number of elements in the center of G plus the sum over all X in R the index of G C X so we see that this is just a reformulation of the orbit stabilizer theorem where we also kind of have singled out the elements in the center because we have there the orbit contains only one element okay so now we want to use this to show that any group which has a number of elements the square of a prime number is a B so we know so let P be a prime number we know we proved it some time that if we take so if the number of elements in a group is equal to P then P is cyclic in particular it is what yeah I mean what it wouldn't make much sense otherwise yeah then G is cyclic so now we want to see what happens for the next case when we have a square so now we want to show if the number of elements in G is P squared then G is a billion or commutative and for this we want to use this result so the first statement is so maybe do I give the definition yeah so first I want to give general definition so if I have a group so P is still a prime number a group P G is called a P group if the number of elements in the group is a power of P if there exists a number N bigger than zero that number of elements in G is equal to P to the N we'll see that when we do the seal of theorems that they also have something to do with P groups contained in given groups so and now the first statement we want to make that the center of a P group has at least the number of elements in the center of P group is at least P so for position let G be a P group so the number of elements in the group is some power of P then the number of elements in the center of G is at least P okay so we want to prove that so we assume that the number of elements in G is equal to P to the N for some N bigger than zero and we know that the center I mean we know the center of G is a subgroup of G so we know that the number of elements in the subgroup always will divide the number of elements in the group for finite groups so we know thus the number of elements in Z of G divides the number of elements in G but obviously the divisors of P to the N are just the powers of P so one P, P squared under P to the N minus one so it follows thus the number of elements in G is a power of P so it would be P to the M where M is bigger equal to zero but it could also be that M is equal to zero so that the center has only one element in which case we would not have proven our proposition so we only have to see so therefore it is enough to see that the center of G is not equal to one that there is at least one non-chival element because we know that the number of elements in the center is a power of P so it must be positive power of P so it's at least P okay so we assume by indirect argument we assume that the center of G is equal to one so in particular the center of G has precisely one element so then we apply the class equation so what does it say? it says that the number of elements in G which we happen to know is P to the N is one one is the number of elements in the center plus the sum over all X and R of the index of the centralizer of X in G where R was a system of representatives for the non-chival conjugacy classes it means that so X are a system of representatives for the conjugacy classes with more than one element or in other words for the conjugacy classes of elements which do not lie in the center of X so here the sum is precisely over those elements for which the centralizer is not equal to the whole of G the centralizer is a subgroup so maybe I can also write this so this is equal to the set of all X so representatives for anyway so I just say it again so if I have an element here we take precisely the representatives for the conjugacy classes for which the centralizer for which the conjugacy class is more than one element so where the element is not does not lie in the center which is equivalent to the fact that the centralizer of X is not equal to G so for X and R we have that the centralizer of X is not equal to G but the centralizer of X is a subgroup so but the Z of X in this case is a subgroup of G so we know that the number of elements in a subgroup is a power of P and so we take P to the N divided by a smaller power of P so the number of elements here will be this index is a positive power of P so we find that for all X and R we have that this index is divisible by P so to say it again we know that this is a subgroup of G which is not equal to G so its number of elements is a power of P which is smaller than this N and so the quotient is a positive power of P this is divisible by P our contradiction we have that P to the N is 1 plus something divisible by P that contradiction P to the N is equal to 1 plus a number divisible by P okay and so with this we find that indeed it's not true that the center consists only of one element and so therefore it is a positive power of P and therefore it's bigger or equal to P and now we want to prove this statement which I announced here that if I have a group such that the number of elements is P squared for prime number then it's a B so the proposition every group of order P squared where P is a prime is a B you know for instance that all groups of order 4 are B and on the other hand we know that the symmetric group in three letters which has six elements is non-Abbian so we take such a group so we have to show we want to show the group is commutative so we can reformulate this in a different way so G is a B and if for all elements X in G we have that the centralizer of X is equal to the whole of G this is just by definition the centralizer of X is the set of all elements in G which commute with X and so if for every element in X the set of all elements which commute with X is everything it means every element commutes with every element so let's see so we want to show that so obviously if X so now if we have such so let's take an element in X in G so if X is an element in the center of G then obviously the centralizer of X is equal to G essentially by definition on the other hand if X does not lie in the center of G it actually will finally not be able to happen if G is a billion but if we assume we have an element X which does not lie in the center of G then it means that if I take the centralizer of X this certainly contains X because obviously X commutes with itself and it also contains the center of G because the elements in the center of G commute with every element but X does not lie in the center of G so this contains P elements so it means it contains these elements all the elements in the center plus also X itself but we know the number of elements of the center of G is bigger equal to P and we so the number of elements in the centralizer of X is strictly bigger than the number of elements in the center of G because we have also the element X so that means the number of elements in Z of X is bigger equal to P plus 1 but the centralizer of X is a subgroup of G and so G has P squared elements and we have a subgroup which has at least P plus 1 elements as the number of elements of a subgroup must be a divisor there is no divisor which is bigger equal to P plus 1 of P squared except for P squared itself so it follows that the number of elements of Z of X is a divisor of P squared so the number of elements of G equal to P squared it follows that Z of X is actually equal to G so we have found that for every element X in G the center is equal to G so it means if you think this to the end obviously we find that this case actually does not occur because the group is commutative we have proven it is commutative so X is always in the center of G because all elements are but we are making an indirect argument so that's okay so this was this result so now are there any questions about this comments or time so now I want to look at something a bit more special I want to look at the symmetric group again and I want in particular to understand the conjugacy classes of the symmetric group so we have talked about the symmetric group in the letters before and now I want to look at it slightly more carefully so talk about the symmetric group as in so we want to describe this group more precisely we will introduce new notations for elements in the symmetric group in terms of so called cycles and then we want to see that the basis of the symmetric group can be described in terms of these cycles the length of the cycles so we call that Sn this was the set of all bijections from the set 1n to itself with the as a group operation the composition sigma tau was equal to sigma composed with tau we have introduced the notation so for sigma we write sigma as some kind of a matrix where we write on the top the numbers 1, 2 and so on until n in the bottom we write the images so sigma of 1 this is certainly a way how one can describe all permutations now we want to introduce a new notation in terms of so called cycles which many of you might also know so you can just say it definition so say let we take some elements a1 the distinct elements of our set 1 to n so we take r numbers from 1 to n different numbers and then the cycle a1 to ar is the following permutation well it's what one might think if one understands the word cycle it means that it should be something which maps a1 to a2 a2 to a3 and so on ar minus 1 to ar and ar back to a1 and all other elements which are not among a1 to ar should stay fixed so this is the map permutation sigma in sn such which is given by sigma of ai is equal to ai plus 1 if for i equals 1 to r minus 1 and sigma of ar should be well maybe just say that and sigma of ar so a1 for i equals r so sigma of ar is equal to a1 so you really have like if you would kind of put them all on a circle you kind of turn it once around and obviously and sigma of b is equal to b for all b which do not belong to the set a1 to ar so this is this cycle so we call r the number r is called the length of the cycle of the cycle a1 to ar and we say that if I have a cycle of length r I also call it r cycle and in particular the two cycles are somewhat more important and they are called transpositions two cycle transposition so you know if you have a two cycle it just means you have two elements a1 a2 and the corresponding permutation kind of exchanges them at least all other ones fixed and now maybe call so we call a1 to ar the support of the cycle and we call some cycles disjoint if their supports are disjoint so cycles a1 to ar b1 to s are called disjoint well if the corresponding sets of elements in one n are disjoint so if and only if if I take the set a1 to ar then this does not intersect set b1 to bs we don't have any common elements so we can first we have an obvious remark cycles are after all these are permutations and it is I claim it is obvious to see that disjoint cycles commute so that means if a1 to ar and b1 to bs are disjoint cycles so this set of these elements does not intersect there is no common elements here are disjoint cycles then a1 to ar times b1 to bs is equal to the other way around that's kind of obvious because what these things do to elements has nothing to do with each other so if I apply this to any element k then if k is among db1 to bs then I will apply this part to it and this will not do anything and this will do the same here and the same if it is one of the a's and if it doesn't belong to any of these it will anyway be the identity so in any case they do the same thing so now we want to show that every element in the symmetric group can be decomposed I mean written as a product of disjoint cycles any unique way every element say sigma in Sn is the product sigma equal to sigma1 times sigma whatever s of disjoint cycles so if we require that so disjoint means pairwise disjoint so no two of them have any element in common no whatever so if we require that if I take the union of the supports of the cycles that this is equal to the whole of the set 1n then this decomposition is unique if we require that the union i equals 1 to s the support so that the union of the supports of the cycles is 1n then this decomposition is unique up to obviously reordering obviously as the disjoint cycles commute I can also order them but I claim that the number of cycles and besides the which cycles they are is unique it's determined by sigma so this second part I will not actually prove so I kind of make this an exercise although it essentially follows from what I prove but and so this decomposition so in this so under this assumption so the maybe I don't need that now it's coming later where is it yeah so we will call so definition so if we have such a decomposition into disjoint cycles such that the union of the supports is everything we call this the cycle decomposition of sigma so in case so composition sigma equal to sigma 1 to sigma n into disjoint cycles with whose union is 1n so such that the union of the supports is called the cycle decomposition so by the buff it is unique so we can look at an example if I have it somewhere well whatever so we can look at for instance let's look at the so cycle decomposition of say the element 1 6 what is it 2 3 4, 5, 6 5, 3 4, 1 so how we do this so we can say we start with the element 1 it is sent to 6 element 6 is sent to 1 so we have a cycle so we have element 6 so if we take the element 2 it is mapped to itself so that is also a cycle now we take the element 3 it is mapped to 5 5 is mapped to 4 and 4 is mapped to 3 so back to 3 and that would be our cycle decomposition so one thing that one should obviously notice is that the one cycle it is just the map which sends one element to itself and all other elements to itself it is just the identity so one cycles are just the identity and so this is why I had to assume that the support is everything in order to get uniqueness otherwise I would have had to assume that it doesn't contain any one cycle that would also be possible and then you can also see that this notation the notation is not precisely unique if you have element 1, 2, 3 this is the map which sends 1 to 2 and 2 to 3 and 3 to 1 but I can also write it as 2, 3, 1 because it is the same thing 1 is mapped to 2 2 is mapped to 3 and 3 to 1 so we can so the the decomposition into cycles is unique but the notation is not unique you can always kind of rotate them element okay so now I want to prove this theorem maybe I first maybe I can first prove the theorem so that's so as I said I wanted to only prove the existence but the uniqueness is actually quite easy so prove so well we will find that so how does one do this what are these cycles actually find is that if you take the element sigma it has the property that it sends an element in the cycle to the next element in the cycle that permutes them so you find that under the operation of the group generated by sigma the supports of the cycle will be precisely the orbits and so that's therefore the way how we want to do it so let h equal to the cyclic subgroup generated by sigma so if I take the map so we have this map of multiplication of elements in 1n by powers of by elements in h so we have the multiplication from h times 1n to 1n which is just we take an element in the subgroup generated by sigma and we apply it to this so tau i is mapped to tau of i so this is obviously an operation of h on 1n basically it's just we have the operation of the symmetric group on the set 1n by just applying the element in the symmetric group to the corresponding set and now we restrict it to the subgroup h so we have an operation and so we can look at the orbits so we choose some elements b1 to b we want it s such that that such that if I apply h to b1 and so on to h applied to bs these are the different orbits of this action so we know that the set b1 to bs is just a system of representatives for the orbits for this action and we know that that that the set 1n is equal to the disjoint union of the set so now I mean I've called h is just all the powers of this one element sigma so let's see we want to so for the i equals 1 to s we choose the minimal power of sigma such that if I apply this power to bi I will get bi back so let mi be equal to the minimum k positive integers such that if I take sigma and apply it k times so sigma to the k of bi is equal to bi you know this element sigma is an element in the finite group so there's some positive power of it which is the identity element and so certainly there is some minimal positive power which is the identity on this one element bi so then it is easy to see that if I take this element bi sigma of bi and so on sigma of mi minus 1 so the mi power of sigma apply to bi these are disjoint distinct elements they are pair wise distinct it's like you are doing some exercise so if if you would have that you know for some smaller number so if two of these would be equal then you could multiply with the corresponding power of so sigma to the L of bi with then it follows that if I take so forth let's say 0 is more than equal then you see that you can just multiply with sigma k to the sigma to the minus k and you would get that bi is equal to sigma of L minus k to the bi and so we have found a smaller power which is equal to bi so we can so these will be pair wise distinct and how does sigma act on them so they are pair wise distinct and we also see if I take the orbit of our element bi I claim this is just this element this is just these elements bi sigma of bi sigma m i minus 1 of bi because in fact what you find is that if you take sigma so in fact by definition if you apply sigma to any element here it gives you the next element and if you take this one and you apply sigma to it you get this so in fact if I look at this set here bi sigma of bi until sigma mi that's one of bi this is a cycle because we see precisely by definition if I apply so let's see maybe I can explain it so if I so I get anyway so if I obviously this is by definition if I write it like this it is a cycle I can write down any distinct elements I get a cycle what I have is that if I take sigma i of so if so if x is an element in the set bi sigma of bi sigma mi minus 1 of bi then if I take sigma of x this will be as I said the next one here so this is the same as sigma i of x if sigma i is the cycle because the sigma precisely acts by you know rotating this by one putting everyone to the next and the last one to the first and this is precisely what sigma i does by being a cycle so so thus we get sigma i for equal to distinct bi sigma of bi until to sigma mi minus 1 of bi for i equals 1 to s are disjoint cycles I mean they are disjoint because the elements here are the elements in the orbit and we know the orbits are disjoint and the union of the orbit is the whole of x so who's such that and the union of the orbits union of their supports is 1n and now if we take any element in 1n I claim that it acts by the product of these cycles so we want to claim that sigma is equal to sigma 1 times sigma s so that this is the cycle decomposition and so we take an element in 1n and so we have to show that these two permutations do the same thing to it so obviously if you apply sigma to it we get sigma of x and if you apply this we get something else so let's see what we do get so let x so we know that the union of these sets here is the whole of so it means that x lies in one of them so then there exists and there's a unique i in so then there is an i in the set 1 to s such that x is an element in the set sigma of bi sigma mi minus 1 of bi well in fact if we take all these elements the union of all these elements is x so we precisely have that x in fact x is equal to bi to the power j for some j with j so not j so now you should protest if I write nonsense so sigma to the j of bi with for some j which lies between 0 and mi minus 1 because the elements here are precisely this bi and then what does sigma do to it then sigma applied to x obviously is equal to sigma to the j plus 1 of bi which will either be equal to bi if this was mi if this j was equal to mi minus 1 or otherwise it's just the next one so the index is like this okay so that's what the sigma does and what does sigma if I take sigma i of bi of x so if I take sigma j of x for k for j different from i then this is equal to x because so this the cycle only permutes the elements which lie in the only the elements which are here so if our x is none of these elements it is not moved by this so sigma i sends bi to sigma of bi and so on but if I have an element which is none of these here it will just stay fixed and on the other hand if I take of x this is equal to sigma i of sigma j of bi and this is just we apply the cycle to it and this precisely says we go one step further in the cycle so this is bi if j is equal to mi minus 1 and sigma j plus 1 of bi if j is different from mi minus 1 and so we see that and so if I take sigma 1 times sigma s of x then these things commute so x is not so the sigma k which are different from the sigma i will not do anything so this will just be equal to sigma i of x and this is which is as we have seen the same as sigma of x so it's kind of I mean I made it maybe a bit more complicated than it is somehow these different cycles have to do with each other so our element x will lie in one of these cycles and then only the corresponding cycle acts on it the other ones don't do anything and therefore we get the same result so this will prove the result so we see in particular that actually in the cycle decomposition we find that the supports of the cycles are actually the the orbits of the of the elements under the powers of the thing we want to decompose so as a corollary we find that every element in the symmetric group can be written as a product of transpositions we see where this plastic is every element sigma in Sn is a product of transpositions so we have so this way for this we just have to see that every cycle is a product of transpositions so assume we have because every element in Sn is a product of cycles so if every cycle is a product of transpositions we are done so we write down any cycle A1 to AR is a cycle and I claim I can write it as a product of transpositions in fact I can just write down what it is so I take A1 A2 A1 A3 and it goes on until A1 comma AR this cycle is in this way a product of transpositions so transposition after all was a two cycle well and you know you can just that's kind of clear so here you want to say that this thing maps A1 to A2 so if you take A1 A1 is mapped to A2 then A2 never occurs again so A1 is mapped to A2 now A2 is mapped to A1 here and A1 is mapped to A3 but then A3 never occurs again so A2 is mapped to A3 and so on so it's easy to see so this is easy to check so this shows that is a product of transpositions and as every element in the symmetric group is a product of cycles we are done how much time? basically none let me see so I maybe just give a preview so now we want to use this to describe the conjugacy classes I mean as I said I will only say so we will find that if I have two cycles of the same length then they are conjugated to each other and if you have a if an element in the symmetric group has a cycle decomposition such that the lengths of the cycles are the same for both if I have two elements which have cycle decompositions with the same lengths then they are conjugated to each other and vice versa so that means conjugacy class of an element will be determined by precisely by the lengths of the cycle in the cycle decomposition of the element and if you look here so such a cycle decomposition is a decomposition into the wet set one you know in particular if you take a support of the cycles this is a decomposition set one n into this joint subsets so the number of elements in each cycle if you take the tuple of the number of elements in each cycle this is set of numbers which add up to n and you do this up to ordering so you find that the conjugacy classes are in one one correspondence to the partitions of the number n so of the ways how you can write the number n as a sum of numbers and so this we will explore the next time and the other time the other thing we will explore the next time is that we also look at the sign of a permutation so if you have a permutation then I had told you here that it can be written as a product of transpositions and this writing this permutation as part of permutations of transpositions is not unique there are many ways but you find out that you can if you take minus one to the power the number of transpositions you need to write this thing this is something which only depends on the permutation itself the sign of the permutation we will prove this and okay that's maybe the beginning and then after that we'll start preparing ourselves for proving the silo theorem


Haiti is in a state of crisis. They just experienced another catastrophic earthquake this time It was 7.2 magnitude the last earthquake that they experienced was in 2010 and many Haitians still haven't fully recovered from that disaster Many had to flee the country But on top of that they are experiencing political instability and political violence due to the assassination of their president So many people have either lost everything or they no longer feel safe in Haiti because of all of the violence and Thousands have chosen to flee the country and many have come to the United States They arrived in Mexico and then they crossed the border and there's about 14 to 15,000 Currently camped under a bridge in a Texan border town and what they're hoping for is to be able to make their case for Asylum many have been here for days and many are starving and they're hoping for a chance at a new life But before I get into the specifics here I just want to give you a broad sense of what's happening. This is an on-the-ground report That gives us some additional context, but keep in mind by the time you see this video the numbers and details May have already changed, but nonetheless. Here's a general overview of basically what's happening on the ground right now I can tell you this is a very dynamic situation that has changed drastically over the last to 48 hours If you ask a border patrol, they will tell you that some of this may stem back to that 2010 earthquake in Haiti which sent many people immigrating to South America and then following the 2016 Rio Olympics where many of those folks worked they then started that long process north But as what's happening right here right now the only border crossing into Mexico in Del Rio remains closed down and it is a 24-7 mission we're just on the side of the border fence and we are seeing agency after agency drive through this gate Manned by the National Guard you see border patrol trucks. You see customs vehicles here This is just part of the massive response. We've seen from authorities here in response to a group that Essentially tripled in size in just a matter of days go back to last Wednesday the group beneath that bridge about 5,000 strong at last check over the weekend 15,000 people were essentially calling the shade of this border bridge home the goal right now trying to process Every single one of those people some of those bus to nearby processing facilities that are not overwhelmed others being Flowing on what they're calling lateral flights to do that same thing And then we've already confirmed over the weekend that those first deportation flights have already begun Three of which took off from San Antonio to Port-au-Prince Haiti But there are still so many people that whole group that flew back about 300 staff We still have at least 10,000 Haitian migrants beneath this bridge. We were granted exclusive access yesterday had a chance to speak to one woman She said she had been under that bridge for eight days had barely eaten a thing We had seen food and water handouts there set up by the border patrol But I mean the supplies cannot come fast enough right now to try to take care of these people Just minutes before we spoke to you there was an ambulance here outside that a woman from a border patrol vehicle Was transferred into and taken away and unfortunately that has been an all-too-common sight here So this is very obviously a huge humanitarian crisis These people are starving these people are desperate and all they want is to be able to make their case for asylum So of course, you know the very compassionate Biden administration is Greeting them with a welcoming message and is telling them listen We're trying to process your cases as quickly as possible. That's that's what's happening, right? And so the Biden administration is currently trying to direct resources to this area to feed and process all of these asylum seekers Right. No, of course not. That's not what's happening. In fact, the message is the opposite And I think you probably predicted that and you probably knew that I was being facetious Because the DHS secretary sent a very clear message get out. We don't want you here If you come to the United States illegally you will be returned Your journey will not succeed and you will be endangering your life and your family's lives This administration is committed to developing safe Orderly and humane pathways for migration, but this is not the way to do it Okay, so nobody else should come got it But that doesn't change the fact that 14 to 15,000 people are already here and they're currently under a bridge And I would argue that the overwhelming majority have a very compelling case For why they should be granted asylum. So what do you do? What do you do to mitigate their suffering? Well, of course, if you're the United States, you do the most American thing ever you Launch a mass expulsion campaign to send them all back to Haiti as quickly as possible And according to AP this could be one of America's swiftest large-scale Expulsions of migrants or refugees in decades. Yeah, so how do you how do you do this? If you aren't going to allow them to make their case or not allow most of them to make their case for asylum How do you do something like this? Like how do you pull this off in a humane way and the answer is you don't you heard these people into planes Back to Haiti as if they're animals and if need be you literally whip them That's what we're doing. That's quite literally what's what's taking place in the Rio Grande currently U.S. Border Patrol agents on horses are trying to herd Haitians drive them out back into Mexico or onto planes and they're literally physically abusing them with whips vice-news is Emily Green Describes the scene border patrol officers on horseback swinging whips in the faces of Haitians Families with toddlers scrambling across the Rio Grande back into Mexico to avoid being deported Haitian parents crying as they faced the prospect of being deported home to a social and political crisis that seems to see no end Those were among the scenes in the town of Del Rio, Texas Over the weekend as the US government took a hard line stance against thousands of newly arrived Haitian migrants seeking protection The situation is becoming a public relations and humanitarian challenge for US President Joe Biden's administration as images of Border patrol agents on horseback screaming at and chasing desperate Haitians reverberated across the internet quote This is why your country's shit because you use your women for this one officer on horseback shouted at a group of Haitian women Who were crossing the Rio Grande with bags of food showed one report by Al Jazeera the situation along the southwest Texas border at The entrance to Del Rio is becoming a bigger problem by the day for President Biden Who is trying to assert control over the international line while fulfilling his promise to take a more humanitarian approach Immigration well you've already failed miserably on that regard Joe So I mean I don't understand why you even maintain this facade that you're more compassionate than your predecessor when we see scenes of Haitian migrants who are desperately seeking asylum getting whipped by border patrol agents on your watch I mean why even pretend you've already gone full mask off so stop pretending as if you care The truth is the United States government does not care. We don't even care about our own people We're letting thousands of people every single year die due to a lack of basic access to health care due to Housing so of course we don't care about these immigrants. In fact, we don't even acknowledge that they're human beings We treat them like animals quite literally So it's just truly disgusting and to make matters worse as Biden tries to claim or present himself as a moral Compassionate like and moral president He's literally using a rule created by the Trump administration to expel immigrants in a very quick manner So as Julia Conley of common dreams explains the Biden administration launched the deportations of the migrants under title 42 A section of the public health safety act which former president Donald Trump invoked during the pandemic to quickly expel asylum seekers From the country president Joe Biden has drawn international condemnation for continuing the policy Yeah, and I just want to remind you that this is taking place under a democratic administration Joe Biden's administration is literally using a trump era rule to expel these migrants as quickly as possible And you can't expel a large group of people in a compassionate and humane way if you want to do it quickly I mean, it's not a humanitarian thing to do period if they're literally seeking asylum I think that they should be able to make their case But to do this rapidly, of course, there's going to be human rights abuses And so a lot of you are going to see the images which are absolutely disturbing of Haitian migrants being whipped by US border patrol agents on horses And that's gross But even if they weren't whipped by border patrol agents or harassed and assaulted by them They're still being treated like criminals. So so rather than being treated as if they're seeking asylum You know, we should treat asylum seekers with respect and dignity and and respond to their needs But that's not happening. They're reporting that they're being handcuffed and some of them are being lied to So they're saying hey get on this plane We'll take you to florida and rather than going to florida in hopes that their case will be processed at a facility there They're getting deported back to Haiti and Haiti is calling on a humanitarian moratorium on these deportations because they're saying, listen We're in crisis mode currently We can't take in thousands of deportees when we're dealing with the crisis from the assassination of our president with the earthquake What are we supposed to do with thousands of people who are coming back to this country? Perhaps worse off than they were when they left there's no homes for them Like what do you want us to do? So rather than doing the humane thing and at least temporarily halting these deportations The united states government at this point is not doing that and they're making Haiti's crisis even worse I mean, it's not like we don't have the resources to assist them here This isn't that many people in the grand scheme of things at a minimum Perhaps at least try to hear out their claims for asylum because I think that most of them If not all of them will be compelling But I mean if you're wondering what do we do when it comes to these sort sorts of crises There's never an easy answer by now with how old our country is with how many times this has happened and will continue to happen In the in the future especially with the progenic climate change You know, we should have some sort of a system in place But whenever this happens whenever we see a large influx of migrants We immediately freak out and if there's a republican in power Then that republican president is going to be as cruel as possible And if there is a democratic administration in power when this happens That administration is also going to be as cruel as possible worrying that you know, if he's not actually Harsh enough it expelling these immigrants that you know, the insane xenophobic republicans are going to freak out and claim that he's too weak It's just it's so Disgusting so, you know when it comes to the question of what do we do? Why don't we just start by like not treating them literally like animals and whipping them? That's like a really really basic thing to start with maybe don't whip them Maybe acknowledge that like us they're human beings with desires with fears with ambitions And maybe not whipping them is a really great place to start. I don't know. Maybe maybe i'm crazy, right? Now, thankfully lawmakers have spoken out. Alexandria Ocasio-Cortez Ilhan Omar They all have condemned the whipping here because these are scenes that we shouldn't be seeing From a so-called compassionate administration.  So it's just you know over and over again we see this And this situation is only going to continue to get worse as we start seeing the issue of climate refugees pop up So, um, you know if you're disturbed by seeing these images then That's good. Don't try to run away from these images Acknowledge that this is taking place under a democratic administration And use this anger that you're feeling when you see these images To fight for a better world for fight to fight for actually a humane response To migrants, especially ones that are seeking asylum, which is a human right by the way