Right now we're going to talk about something really exciting, subgroups. You know, we've been filling the box, relations and all sorts of things. In the beginning it was boring, we filled it, we don't know where it belongs. We filled the box, we've eventually started looking at groups. Things got interesting, showed you integers, mod n, some other groups. So, you know, we're using stuff out the box, it's getting more exciting, it's getting more exciting and now the excitement just ramps up because we're going to talk about subgroups. So remember g is a group if I have to set a and its binary operation with the four properties. There's closure under that binary operation, associativity holds, associativity holds for any a, b and c element of a. We have a unique identity element called e and then there's a unique inverse inverse for every element, for each element in a. So it contains all its elements and for every element the unique element is also there. One of them is the identity element, there's associativity and there's closure.  Now I can create this subgroup of a prime and that same binary operation. If, you know, these properties hold for this subset of a, the elements in a, then h will also be a group and this will be then called a subgroup. That's the definition of a subgroup of g, the definition of the subgroup of g. All these things must hold though for that to be to be so. Remember I can have two special ones though. I can say that a inverse contains only the identity element and I can have that a inverse, you know, is a equal to a and yes, that will make a subgroup of well of h but those are called improper subgroups sometimes and that's not the ones we are after. We are after taking some elements out of a so that it is a proper subset, compion empty set and not one of these two and if I have that same binary operation, they've got to be the same and all four hold then h is a subgroup. That's our definition. Turns out though, I actually don't need all four because there's this following theorem, a non-empty subset h. Now here I just used the a and the subset of a. I'm just going to shift a bit and just call this thing the g and h both a set and group. I'm going to use the term interchangeably for these and please just know that it includes the binary operation as well. So I'm going to say a non-empty subset h of a group g is a subgroup of g if and only if the closure property holds. So if a and b are an element of h then a b and that should be a with its binary operation there. Most of the time we just leave it out as an element of h and every element of h has a unique inverse in h. So if a is an element of h it implies that a inverse is also an h. Turns out if those two things are true then h is a subgroup. I don't need this one and I don't need this one. Let's prove this and as I say that's why this gets exciting because we're going to do proofs and I'm going to show you actually just how easy it is. Because we have an if and only if statement it goes both ways. You've got to prove you've got to take this and prove this you're going to take this and prove that. Let's do it in the what's sometimes called the forward direction. So I'm given that h is a subgroup. It's the easy part so given that h is a subgroup then by the definitions of a subgroup which I've just given it to all four holds meaning those two hold as well. Given that h is a subgroup by the definition of a subgroup by the definition of a subgroup you can write those two properties do hold. So it's proven in that direction now for the interesting one let's prove it in this direction. Given that I do have this closure property so I'm given that there is this closure property. Can I prove can I prove then that given these two what I'm trying basically to do is given these two can I prove that all four of them hold can I prove that all four of them hold. So I need to prove this associativity and I need to prove that the unique element is also an h. Given just these two facts can I do that well let's say for all ab and c elements of h given that it because it is a subset you can write out the words nicely it implies that ab and c are also in g because h is a subset of g and g is a group we were told that is a group so because it's a group abc equals abc because that is a group so association holds but that same abc is also in here so associativity holds for a we were given this one we were given that one I just showed that this one is implied let's look at the other one that the unique I'm told that every has its unique there so for all a element of h it implies that a inverse is also an h because I'm given this does this help us make a group well we've just we've just been told or let's just remember by definition if I have a inverse and a I get the identity element I am given the fact that the closure property does hold that means e must be in there therefore that implies e is an element of h so we also have that so given just these two all four of them are there and that implies that h is a subgroup I've proven it QED I've proven it in both directions so the proof is very very easy so now we know if we have this group g and if we take some of the elements out and we keep the binary operation the same if we look at this new subset h and only these two properties hold we know that that subset and its binary operation does form a subgroup and the proof is very easy I'm going to clean the board because it turns out this is not the only theorem that proves that if I have a subset and the same binary operation not only this one there's another way to look at it as well which also will prove that that is we'll show you that that is also a subgroup and that's a different theorem it's clean the board and we'll do that one so let's have a look at this theorem it also says a non-empty subset h of group g as you can again see I'm using this notation of its subset in a g interchangeably because we're sticking to the same binary operation is a subgroup of g if and only if so I've got to prove both ways for all ab element of h a inverse binary operation b is an element of h so first glance this looks a bit different from the previous theorem but it isn't actually because what we are hiding there is the same it is the same thing that we are hiding so the proof in the forward direction again is very easy because I'm given the fact that this is a subgroup therefore all the properties would hold therefore these things would hold and in reverse what we're actually showing here is that a is an element of h and a inverse is an element of h you know that would imply that by the same way we did the previous proof that e the identity element is also and I needn't stick to ab and c you know ab that could have also been a c so c inverse b would also be so by the same token I have ab and c in h and therefore they are also part of ab and c they're also part of g and since it is a group that means since since it is a group it does mean that this associative property would hold and it's going to equal abc so I'm just showing these other two so it's just a different way of writing but the same implications as the first theorem I just are in there in the statement that you have here as well so the proof other than putting the words out nicely so you sound like a mathematician the concept of these proves are actually quite easy so let's just go on just to look at so and actually I hope you understood those two proofs they are really really simple if you think about it again you are given some stuff we have made definitions those definitions that we make remember they are you know that's what we come up with we decide that as humans that is our definition and the tool set that we have in these definitions we just use them and build new stuff so we put a theorem out there we prove a theorem that's something new that goes in the box and we can from now on just use that we get that that's a subgroup because we've already gone through all the steps of you know using prior definitions prior things things that we've put into our toolbox now this this goes into the toolbox both of these theorems and we can just use them and now we can use them and the next proof because we've already proven them let's look at some examples okay so let's make my group G the A and the binary operation and A is just going to be remember the all the all the fourth roots of one and they were remember they were minus or they were one so that equals minus one one minus one i and minus i those were the four and if I were to have a prime only be one and minus one and my operation that I still have a still multiplication and here it was multiplication for a multiplication is that still is that still now remember I only have to show let's use the second one and so A equals one so A inverse what is its inverse it's also one and B equals minus one so A inverse with B A inverse is one minus one one times minus one that equals one so low and behold this is if I just took those two that is a subgroup okay let's do the following let's take the integers mod four the integers mod four remember those we're just going to be my equivalence class is zero one two three remember those so if I were just to take if so that's my group so my or let's say my group is z four under addition and my A is that and let's make my A prime just going to be zero and two and let's have a look at that let's see let's do a Cayley's table of that we have addition we have zero and two zero and two zero and zero is zero zero and two is two zero and two is two and two and two is four which brings us back to zero which is there so there we go that's my Cayley's table so all I said is I wanted closure and is there closure yes any of the two that I do the solution is also part of the subset so I have closure and the other one that I want everyone's inverse must be there and so something with something must give me the identity element and we know the identity element here is zero if we look at this we just look at this we see the identity element is zero so zero is its own identity element and two is its own identity element because two plus two is zero so I only needed those two all the other two of my four properties hold by the theorem that we've stated and so the fact that I should just call this h or so that is this is g so if h was a prime under addition it means h is a subgroup easy to show that that is a subgroup so in short that those that is subgroups very interesting stuff and it gave us this opportunity to look at proofs and just to show you how easy those proofs are never be afraid of proofs just do so you know as more that you more more that you do the better you'll get at it and it really is easy they don't think you'll forget the concept of those two proofs they really are simple just what does in your toolbox the properties that we have decided as far or the definitions that we've decided that is what we would call a subgroup use that what's in your toolbox and the proof will come and there's two beautiful examples of subgroups


I destroyed my family with my affair. As my last resort, I had to make my husband an offer he couldn't refuse. But I never expected he would use it to checkmate my life. When you cheat on a Sigma and offer him a queen to lure him back in, beware that he might be a master of the game. Warning, the following story will make cheaters rage quit. Hey there! Thank you for reading my post. I'm in a somewhat unique situation and wanted to see if anyone else has gone through something similar. I'm not the victim here by any means. The victims are my husband, my kids and my parents who are living with the burden of my past sins, for which I am truly sorry. Let me be blunt. 19 months ago, I was caught having an affair with a married neighbor and father of three. I'm a 32-year-old female. My husband is 39 and the neighbor in question was 27 at the time. For confidentiality, I'll call the neighbor Steve, my husband John and myself Amy. As stated, I made a terrible mistake having the affair with Steve, which began a little over two years ago. While the affair lasted nearly five months before we were caught, I was only physically with Steve four times in total. I know readers here are not going to believe that, but I swear this to be true. Now to answer questions about my marriage that I know everyone reading this has. Were we having problems? Did I not love my husband? Was I unhappy? The answer is a resounding no to all. I was completely happy and fulfilled with my marriage and I love my husband and our two boys, ages 9 and 11, more than anything in the world. I was totally satisfied emotionally, mentally and physically by John. He was all I ever dreamed of and so much more. My misplaced attraction to Steve happened from a deep place that took me back to my first romantic encounter when I was 18. It was a feral attraction. Just like my first time. In high school, I dated four boys, but nothing serious beyond a quick kiss at the end of the night. In fact, I viewed all those guys as friends since we all grew up together. Then one day I was invited to go to a barbecue that my friend's parents were having. There I met Charles. Charles was my friend's cousin. From the first time I saw him, I was taken. At the time, he was 20 and I was 18. From the moment we met, we couldn't keep our eyes off each other. I don't know what it was, but there was just something between us that drew me to him like a magnet to metal. We started talking at the barbecue and he had to leave for work so we exchanged numbers. The following day, Sunday, we met for ice cream in the evening and took a walk. We talked for hours, totally immersed with each other and just spontaneously started kissing each other. He invited me back to his apartment and there I had my first experience. It was magical, better than I ever dreamed. Something about Charles just excited me and made me want to give him every part of me. To this day, I can't describe it. It was subconscious. I couldn't resist. Beyond the physical relationship, we had absolutely nothing in common. In fact, we were actually incompatible. I broke it off with Charles 11 months later, after the passion wore off. A year later, I met my now husband, John. While Sparks didn't fly early on with him like they did with Charles, over time I developed a deep love for John that was beyond anything I had ever felt. He checked all of my boxes and I knew he was the one. We were married a year later and our marriage had been 13 years of joy until I destroyed it. We were blessed with two wonderful boys that are the spitting image of their dad and have his awesome personality. I've given you all these details because they are relevant to why I started the affair with Steve. Steve and his wife, call her Erica, moved into our neighborhood. They were the youngest couple in the development and were quickly welcomed by all the neighbors. Surprisingly, my husband and I are the second youngest couple with the rest being in their 40s, 50s, and a few in their 60s. Steve and Erica were invited to a neighborhood picnic and it was there that he and I first locked eyes. It was exactly the same vibe I got when I first locked eyes with Charles at that family barbecue so long ago. The next time I locked eyes with Steve was at the car dealership where he worked in finance. We were in the market for a new SUV so at the picnic was when my husband found out Steve worked at the dealership so they naturally started talking. We went the following week to look at cars. Steve made sure the salesman gave us a good deal and Steve got us great financing. Throughout the closing process, Steve and I were making eye contact with each other but my husband didn't notice. A few days later, I had to bring the vehicle back into the dealership to have mudflaps installed and it was there that Steve and I had our first inappropriate meeting. When he saw me in the lounge, he came out to greet me. He asked me to come back to his office as he had some additional information about the financing to discuss. We sat down and he got coffee for the both of us and we started chatting just like I did with Charles. He then just blurted out and told me that he wanted to speak to me alone to discuss how he was feeling about me. He said he felt such a vibe and said he noticed me glaring at him. I told him I feel something but it's wrong. He said he knew it was wrong but didn't care. He said he wanted me. Fast forward to the following morning when we had our first intimate engagement at his house after our kids went to school and our spouses left for work. By the way, my John has a good job and Erica is a licensed nurse. As I stated, Steve and I only had physical relations four times during the entire five month period. There was absolutely no love connection between us as I loved John and Steve loved Erica. What we had was just physical and I have to be honest, the physical part was not as good as what I had with my husband. Not even close but it was forbidden but it was thrilling and dangerous, I guess. Looking back now, I think being a stay-at-home mom for 11 years made me desperate for the attention I was getting from this attractive younger man. I just thought I could have this secret adventure for a while and still maintain a loving and fulfilling marriage with my husband. That thought all came to an abrupt end one Thursday morning, 19 months ago. It was then that Steve and I were caught in bed at his house by Erica's mother. She walked in on us while we were fully engaged and just started screaming obscenities.  She also hit me square on the jaw and pulled out two handfuls of my hair before I could gather my clothes and get out of the house. When I got back to my house, I was in total shock at what just happened and the reality of what I had done set in. I knew my fairytale marriage with John was changed forever and could end because of this. I sat silent for a couple hours just staring at the walls wondering what I was going to tell my husband. I then decided to call him and left an urgent message. I said that I had something very important I needed to discuss. He didn't respond so I texted him and still got nothing back. At this point I knew that Erika or possibly even Steve had likely gotten to him. A few minutes later Erika and her mother showed up on our front porch and started banging on the door and on the bay window screaming for me to answer. I didn't. They were yelling obscenities and said they knew I was in there and demanded me to open up. I was scared beyond belief and thoroughly embarrassed. Thankfully my boys were at school they finally left and I laid down on the couch crying. I fell asleep briefly and was awakened by the sound of a car door in the driveway. I looked out and saw my husband. I ran into the bathroom to splash my face and look into the mirror before going back into the living room to greet him when he opened the door but he didn't enter. Instead I saw out the window that he was walking down the street towards Steve and Erika's house. I watched him as he walked down there and entered where he stayed for nearly three hours before coming home. When he came home I went to hug him and he just kept me away. I then started apologizing and he said that my apology was not accepted and he wanted me to leave now. I fell to the floor crying and begging and told him I didn't want to go but he insisted. He then called my mother on the phone and told her what I'd done and asked her to come over and pick me up. When she arrived she apologized to Steve and forcibly convinced me to go back to her house for the night. She then helped me pack some clothes and I left crying asking John what he was going to tell the kids. He said he would take care of it and I left broken hearted and ashamed. That night I called John and to my surprise he answered. When he did he just said hello and went silent. I told him it was me and that I was so sorry and that I would never do something like this again. I also told him that I will spend the rest of my life making it up to him. John said nothing and just asked me if I had anything more to say. I said no and asked him what he was feeling. He told me, you know what I'm feeling and I started crying. He then said he wanted me to stay at my parents' house for a couple weeks before I came home. I reluctantly agreed but asked when I would get to see him and the boys again. He said he doesn't want to see me now but agreed to have a brief call with me every evening at 9pm. We ended that first call with me saying I love you and John saying nothing just hanging up. Our call the following night went the same with me apologizing and John being silent until I quit talking. He then told me that he wants a divorce. Hearing this I melted and begged him for another chance. He refused and said he knows he'll lose half his hard-earned assets. Then in the next breath he said he'd give me everything he owns if I just disappear and leave him and the boys alone. I broke down and told him you don't mean that John and he said that yes he does. We ended the call and I cried all night. I then started thinking of what I could do to make him stay and came up with a plan to offer him a post-nuptial agreement that would be so favorable he couldn't refuse it. All I wanted was to get a second chance to prove my love to him no matter what the cost. The following week while John was meeting with his divorce attorney I was meeting with a divorce attorney myself not to prepare for divorce but to create a post-nuptial agreement to present to John before I received the divorce papers. I went to four different attorneys before I found one who specialized in post-nuptial agreements and who was willing to create such a lopsided agreement. Lopsided in the sense that my husband would receive nearly all of the benefit in exchange for remaining married to me for a period of time thus giving me a second chance at love. Unfortunately John's attorney completed the divorce papers in just 11 days and I was served at my parents' house. Two days later I had John served with the proposed post-nuptial agreement. We talked that night after he read the proposal. He was a little surprised at what I had offered and for the first time I could sense the caring person I once knew coming through not the angry man who had been so robotic and cold for the past two weeks. Financially and personally the agreement is a complete and total win for John and an opportunity for me to prove to him I'm worth keeping. I'm not going to get too specific on what the post-nuptial contains but I will confirm that it does enable John to keep nearly all of our marital assets if we stay married and living together for at least 30 months. Additionally if I were ever to be unfaithful again and we divorce I lose all claims on our marital assets I get nothing and forgo any alimony and child support payments. The agreement also calls for me to get a full-time job within the next six months and begin contributing to an appropriate share of our household expenses. Finally my husband can see other women if he chooses throughout the remainder of our marriage. I know John would never be unfaithful it's not in him but I want him to know I love him enough to give him this option. To my surprise and delight John accepted the offer with one additional stipulation the clause John wanted added stated there is no requirement for us to sleep together or to have any type of marital intimacy during the remainder of our marriage I was saddened and hesitant to agree to this but finally did as I felt that with time I would win back his respect, trust and love. Things have not gone as I thought and that's why I'm here. We are now 17 and a half months into our second marriage as I call it and our relationship is one of being housemates raising our boys. Don't get me wrong I thank God every day for the second chance I've been given love wouldn't qualify as a marriage it's more like we are two divorced people cohabitating. Since my affair John has shown absolutely no affection towards me whatsoever and I mean nothing not even a kiss or a hug he won't let me near him to express any type of affection although I do get in for a hug and kiss occasionally before he can block me but I can tell he doesn't like it so I don't do it very often even so he requires me to submit to monthly at home STD testing. Also since the affair John will not go out in public with me even to family events. When our boys have games we alternate who takes them. When it's my turn John shows up at the games but doesn't sit with me. Instead he normally stands on the sidelines with other fathers and acts like I'm not there. The only time we go out together is when we go out of town or on vacations which we do often. When we travel he orders adjoining rooms between two queen beds each. The boys stay in one room and we stay in the other in separate beds. I look forward to every trip as these are the times we are closest and where I've almost broken through to him. I've pointed this out to John and have suggested moving from our neighborhood as I know if we did we could start anew. John refuses and says the only way he will move from the neighborhood is if he gets a job promotion which requires him to relocate. If not he plans to stay in our current home until our boys graduate high school. The boys don't want to move either as all their friends live within a half mile of our house as does all of John's friends. Talking about friendships since the affair I've lost all the friendships I had in our neighborhood. Steve and Erica divorced 8 months after D-Day but Erica and her kids still live in the same house down the street. All the neighborhood women I was once so close to have basically cut me off and blame me for breaking up their family.  My boys are always out in the neighborhood or they have their friends over at our house including Erica and Steve's kids. Thankfully nothing has really changed much in their little world. John does the same. He's good friends with all the neighborhood men the guys are either over at our house smoking cigars and sipping bourbon at night on our back porch or he's at one of their homes. John basically goes to work then to the gym and then comes home. He fixes himself something to eat and then it's off to a game or practice or he's socializing with friends. He doesn't eat dinner with us and will not eat anything I make anymore although he did sneak a few cookies I made the other day.  The weekday dinners I have with my boys have been a great bonding experience for us. They like to eat shortly after getting home from school so the three of us normally have dinner around 4 p.m. I have everything prepared and they set the table help me with final food prep then help clean up after dinner. I cherish this time as it has really brought us closer and has taught them valuable skills. They even help me in the garden where we have created an awesome space in our backyard with landscaping. So in summary some things in my life are really great while some aspects are just awful. I guess this is just a long way for me to ask whether you think this marriage is worth continuing as is or if I should just let John go now and give him the financial benefit as if he'd stayed with me. I know deep down he's not happy. How could he be? It's clear he no longer views me as his wife or lover just as a co-parent which we are both great at by the way.  I want nothing more than to get back to the loving relationship with him I once had but I don't think he will let us go there. Let me know what you think I should do. I'd really appreciate any suggestions anyone has for how I could successfully earn back the love and trust of my husband after betraying him so brazenly. Thank you. Amy I think in your case what will draw your husband back to you is distance. You should stay married but separate for a while. Rent an apartment somewhere nearby so you can still have that quality time with your boys. As they say, distance makes the heart grow fonder and I think John will quickly realize this. I do hope you work things out as you seem so well matched. If you really love your man as you say you will set him free and allow him to keep the majority of the fortune he built. You've already taken his pride and dignity and destroyed his soul isn't that enough for you? He'll never trust you again because you are untrustworthy. If another Charles or Steve should cross your path in the future you'll do the same damn thing. It's clear that you are physically attracted to a certain type of man also that you are mentally attracted to a certain type of man with Charles and Steve being the former and John the latter. In your 20s and 30s that physical attraction is much more powerful but I assure you in time the mental attractiveness and love of a good man like John is far more important. Hang on to him if not for your own sake as growing older peacefully and for your own interests. Women like you are the reason I've not yet married it amazes me how you can go for years being a loyal wife and then immediately hop in the sack with any strange man that gets your tropicana flowing I just don't understand this I encounter beautiful women all the time but I would never think of doing anything with them because I'm in a relationship with my girlfriend good grief. First update, seven weeks later I've come back to give an update on my situation last month I took the advice that a number of you gave me and decided to move out of the house for a while to give our marriage some space I got a short-term rental on a nice furnished apartment nearby and have been living there ever since while I miss not being in the same house as my husband and boys and miss my garden it has been a relief getting out of that neighborhood there are just so many terrible memories and bad vibes there which I know are my fault I'm not excusing in any way what I caused when I broke the news to John of my decision he seemed surprised and a little saddened and asked a lot of questions his reaction told me a lot it told me that he still loves me I saw it in his eyes I pick up my boys after school and they come here and eat dinner with me and spend the night a few days a week John and I are flexible on that and they can come and go as they please at either place the real issue I have now is that since I'm out of the house I don't get to see John much at all nor am I in a position where I get to talk to him so I end up calling him asking stupid questions multiple times a week just so we can keep in touch we've had a number of long conversations about everything and nothing at all recently which is another indication that he still loves me I know I love him that's all for now thanks and take care final update five months from last update I've delayed coming back to update as I wanted to give time to enable me to provide a complete perspective to my situation what a journey talk about a roller coaster life definitely has its ups and downs first the downside after two years into our second marriage John decided that it would be best for us to divorce John said while he still loves me he would probably reestablish a romantic relationship at some point in the future he just can't do it while we're married I don't understand what he means but he explained it's something psychological he said while we were still married he feels disrespected and betrayed but after we divorce he thinks he can let those feelings go he said it would be like dating again and promised me we would go out to celebrate our divorce the day it's final and possibly spend the night together I know this sounds like a crazy ploy to divorce me without guilt on his part but I'm up for it if it means I can keep this man in my life as my partner, lover and friend if we do reconnect John made it clear we will never get remarried he feels if we truly love each other a binding contract isn't necessary I agree with that statement but I do wish there was some way he could do this without divorcing me as for the divorce I'm voluntarily letting him keep 75% of our marital assets even though he didn't fulfill the stipulations in the post-nup I'm also not going to pursue alimony or child support from him I know there are women out there who are going to read this and chide me for being so giving but I feel he earned the money and would have given all of his fortune to me if I had remained faithful to him I'm at peace with this decision even with the reduced settlement I'll be able to live comfortably for the next 8 or more years without working but now I am actually working so I'm in an even better place there in closing I just want to thank those who sent me responses you don't know how much your words guided my actions and helped me through this difficult time before I sign off here I wanted to give some advice to women out there who have difficulty controlling temptation as I obviously do my advice to you resist don't do it the thrill is not worth the risk if you feel you can't keep yourself in check seek professional help I can assure you from experience the short term high is not worth the long term loss of love, respect and trust my best to you all that brings us to the end of Amy's story she said she loves her husband and two kids but that love wasn't strong enough to overcome her feelings of lust actions speak volumes stories like hers do you think that John knew what he was doing I'm sure he did and he was strong willed all the way through he does sound like a strong man willing to endure the betrayal to end up on top in the end or do you think he really was giving Amy a second chance I wish we had his side of the story but we don't unfortunately I'm curious to know what you think share it down below thank you for staying till the end you're the one I make these episodes for don't forget to find the like buttons vacuum and flip the suck function to blowing see you in the next one


Russian President Vladimir Putin raised the prospect of reading a nuclear deterrent in order to distract from a lack of progress in the invasion of Ukraine. British Defence Secretary Ben Wallace said these on Monday. Reminded everyone he's got nuclear weapons which as you say starts to set off people being worried but secondly he distracted from what's going wrong in Ukraine. You know we're all talking about it we're not you know he is clearly wanting to get people's attention distracted from what is going on on the ground and he's had that you know to some extent he's successfully had it. This is the overwhelming scale of the Russian Federation Army up against Ukraine. They are behind schedule they are taking significant casualties and they are feeling public rejection in parts of the Russian system itself we've seen many protests but the Russian handbook is to then get more violent and commit more forces because fundamentally in the Russian sort of doctrine the the lives of their own soldiers matter much less than in other armed forces so we have to brace ourselves for what may come next which could be ruthless indiscriminate bombing of cities and the propelling forward of soldiers and high casualty levels and that's going to be horrific hello hope you enjoyed the news please do subscribe to our youtube channel and don't forget to hit the notification button so you get notified about fresh news updates


Hey everybody, it's great to be here and you know thank you very much for the introduction. I'm really happy to tell you about a very new program that we have launched in collaboration with many other organizations and we hope more soon including those here that are not yet part of our little endeavor. We call it the AI Alliance and I'm going to tell you about the program but first I'm going to tell you about why we came together to do this. If you remember the beginning of this year and it was a long time ago it was a strange time for AI, wasn't it? Because AI has been very open for many years, software, open science, research and it was very collaborative but in the last couple of years that started to switch and change and early this year it looked at risk of really changing, proprietary models risked kind of taking over. In fact if it was in the spring and you were a developer you wanted to build the Gen AI application you pretty much started with an API tying into probably one proprietary model set. Now that's a pretty striking contrast actually because the last months have been really great for open source. There's a couple of compelling examples. You've heard about a lot of this already but I just think that they're illustrative of what's happening. Lama, Lama 2 with the permissive license was only released in the summer, it's only been a few months and in that time it's been downloaded over 100 million times and there's a whole ecosystem of tools, of variants growing up around it. That's not like years, that's months, it's pretty incredible if you think about it. A few other examples, you've heard about some of this today but if you look at just these two application frameworks, helping developers that want to get started trying to build an application of Gen AI like 95,000 stars in again six to nine months. That's pretty unbelievable. You've heard from Jeff earlier, Hugging Face, right 300,000 stars, 400,000 open models. You all don't need to be convinced that the community wants more than just a managed service API. But there are lots of headwinds still, we shouldn't joke, we shouldn't kid ourselves that everything's good and be complacent. There are actually lots of challenges still to open source AI. It starts with the resources required. It's still the case that if you want to build especially at the leading edge of model capability, it takes a lot of resources, it takes a lot of money, that is excluding a lot of people, especially researchers that need to be part of this. Things have changed a lot too in terms of building applications and it changes all the time, right? The patterns are the thing today but there are a million different varieties of how to do that. Things that you optimize for one model family are not portable to another and so on. And then there are safety and trust concerns, a lot of really legitimate, serious concerns that need to be addressed with practical solutions and some hyperbole too of course, which we need to try to distinguish between. And then in terms of legal and regulatory environment, there are also challenges in terms of copyrights, challenges in terms of new regulation, which we'll get to in just a second, that threaten to restrict what you all do. And then there's this interesting, mostly productive but sometimes unproductive debate happening about what is open source AI? What's good enough to be called open source AI? Look, this is a very generally healthy thing but let's not get too caught up in what open source AI models should be just yet. Let's work this through and let's also celebrate increasing steps to be more open in more ways. Now, always fun to have a few numbers to attach to these statements, right? What does it take? Well, it takes still to build a model, a lot of compute. It takes compute measures in hundreds of thousands of GPUs. It takes time scales of order of weeks. Those are numbers that are millions of dollars. Now, that is simply hard for organizations and especially the research community to deal with. If you think about what it takes in terms of data, Chinchilla scaling laws show pretty clearly empirically that you need multiple trillions of tokens of data to train a model at the leading edge. Then there's a whole different variety of challenges, as I mentioned. There are, in case you haven't been paying attention, vigorous debates in many parts of the world, especially here in the US, about what we should do to regulate AI. Just last week, the EU has decided to move forward on their AI Act, which is actually reasonably encouraging, I think, from an open source standpoint. Now, we have to see how things evolve. But for a little while, there was a real risk that open source would be greatly restricted and that risk has not gone away. Here in the US, there are very active debates about what we should do to regulate AI. And there are many people that are threatening to really put a damper, to put a restriction on open source work in AI. Because what's happening is to some success, people are arguing that open source is much more dangerous than a closed source solution, which is kind of crazy if you think about it. But that argument is holding sway in places. And then there's this. This is a great one, right? Do we all have to confront the fact that we're contributing to an existential risk to humanity? No, no, we don't, okay? If we take a step back and you think about what's happening here, there are lots of legitimate, serious, important challenges and risks of AI to solve, but they're much better solved in the open. And these arguments that are getting put forth, somewhat successful in policy circles, that AI represents an existential risk to humanity, is frankly a lot of nonsense. Now, for all of these reasons, a number of us have come together to create an umbrella program we call the AI Alliance. And the Alliance mission is to support, is to enable open innovation, open science, open source in AI, and to do that inclusively, to do it globally, and to do it in a way that we can make reality continue for what we all have known for a long time. That open source provides far more benefit than it offers in terms of drawbacks. Now, the program is straightforward. We are bringing people, we're bringing resources, we're bringing data, we're bringing compute together to enable building and supporting open technology development with the simple goal of across the stack making sure capabilities in the open are just as good, if not better than any proprietary capability. We are going to be enabling developers, educating students, we're going to make sure that these technologies are accessible and usable and understood. And we're going to advocate, not from the sidelines, but very directly to make sure that every policymaker and every business leader and organizational leader understands clearly why open source in AI is so important and why it really is the solution to many of the practical problems we have and not the danger. Now, we just announced it. This is actually the first public talk other than some media announcements. This is the first public talk about the alliance. So I'm testing some messaging. If it's not resonating, I'm going to, you know, let me know and I'll tweak it next time. But we just announced this. My favorite headline is right here. Open source AI fights back. I love it. Lots of other headlines. It has gotten more attention than, you know, even an IBM marketing department could hope for. And that's a lot of attention. I'm going to tell you that. We're really happy that this is getting the world's attention. We're happier that a lot of the core messaging has actually come through here, right? Supporting open source, focusing on the benefits of open source, there's a fun little battle that, of course, has been set up, as you might imagine. But that's not entirely a bad thing. Now, as I mentioned, we wanted this, even from day one. And we plan to grow it. We plan to add many more. We plan to expand the program. But even from day one, we wanted to try to be representative of the diverse community that exists in AI and in open source. So we tried to do this quickly. We've got a number of organizations globally, as you can see here. They do span research organizations, universities, large companies, startups. We cover a number of areas of the world. There's more to do here. But we're happy with the starting point we had. And if you look through this list, there are many names that have been represented at this conference here. And so you've already seen a piece, many pieces, of what this alliance is building from. And if you think about the program vision, imagine we're going to be bringing things together and enhancing and growing. And we're going to do it with this base. And we're going to do it even broader as we move forward. Now, I'll just take a few minutes, or a minute or two, to go through the program itself. So what is this? This is a broad program. And it's structured in terms of an alliance of projects. And it is very self-driven. It's not a monolithic program. It's not modeled after a traditional open source organization necessarily either. This is a program that's based around self-driven and organizationally driven priorities. It will be composed of projects. Projects are going to be spanning the six categories on the right, which I'll mention in just a minute. And importantly, this is very much about what individuals or organizations would like to prioritize, what resources they're going to bring. And as such, different organizations can take part in different projects as they see fit. There's an agility built into the program and a lightweight kind of approach to the overall governance that we're going to try to maintain very strongly. Now, if you look through the categories, we are fairly ambitious here. We want to work across the stack and across the ecosystem that starts with education and skills building. So a number of our organizations have already made strong commitments and have a lot of activity here. We're going to be expanding what we do here. And in particular, bringing resources to the challenge of enabling exploratory research to continue at the leading edge. We want to, number two here, build solutions to the challenges of trust and safety in deploying AI. There are real issues here. And we want to build real solutions, right? We don't want to be focused on hyperbole. We want to build tools. We want to build standards and benchmarks. We want to do that collaboratively. And we want to then obviously show the world that, practically speaking, open source can solve these problems. We then want to make sure that we continue to build out the very important existing frameworks and new frameworks and software projects that are enabling model development and application development. We have an important thrust in number four here to enable choice, to enable the democratization of access to different forms of hardware that are rapidly advancing and becoming part of the scene. We absolutely are going to enhance and work toward better open foundation models. And I'll just point out one really important part of this, as I think you may realize. But just to be clear, there's a lot of languages and cultures in the world that are not included in the LLM revolution yet, whether because native language data sources are not good enough or not really available enough or because alignment and tuning principles don't aren't established for different cultural norms and so on. This is a really important thing, and it's a topic that many of the members in the broader, especially outside the English-speaking world are extremely interested in. And finally, the advocacy piece, super important. We need to make sure that our elected officials, that our policymakers understand the importance of open source AI and why it is essential to have a healthy and very open ecosystem. So I am going to leave it at that. If you'd like to learn more, check out the site. I'll be around afterward. I'd love to talk to all of you. As mentioned, many of you are kind of part of this already. And if you're not, let's talk. This is just the starting point. We have a lot of big things planned, and we'd love to have you contribute to it. So with that, thank you for your time. Hopefully I get a chance to meet some of you after.


రార్నకాత్త్ గోకలార్నింిసివియ్క్మాచార్క్ర్ధానన్లండివంాచా, ఆట్త్సాటార్యారికొడికు. మనోత్టలాటా, మనోత్త్చారె  estable reme  emergencies                                                                                ��ठीवाण ढीन की अचलाः शीदा आप या ळ हमावि आप य जो आप पहाटना छीए ञाजा कोका इूए तेश्विन अप चराजाच ऐम आप वोग � nazi-a-ha-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a- యాంటంనింపోరగ౉ ఆరజొసాడిలిటించ౔ం షిగాసిలికిహాలె. పనిన౜సికాకిది హికికికరిడి కినికి. గాకనిపనికనినాకికి కికని . and that it has brought untold hardship on Nigerians and that the president should revert to status quo. To do the iron loads, 1,900 iron loads are the ones that people have more than the children iron loads. Also the problem is that the ATMs are not configured for children iron loads and of course they have to take a route to configure the other ATMs to start dispensatory iron loads. So we are only compounding the problem. We are not solving the problem, we are compounding it. And we do know that we feel it are the avid Nigerians. Everybody was taught and was covered literally who was the brain behind all of this policy. And we can see that clearly is the voice of Jacob and the hand of Isso because you can see clearly that the president is the mastermind of all of this activity. Even though there are conspiratories about whether or not the policy is aimed at ensuring that politicians do not spend money on election day or all of those things any policy that is to be introduced but first they get to account the reality of these people the reality of the avid Nigeria, the common man who agrees to transact towards a good business on a daily basis but they don't have the luxury of having an account besides bringing money to their house. So you have the politicians who this policy is aimed at. I mean I did see the civil and government explaining the policy and its benefits but of course those are the policies aimed at have the means of getting back this money but they have the means of getting these new notes I do not have more than 100 million units in the wallet I don't believe that you access the new notes and the new transfers and the transfers on the engine they may fail in the engine so what exactly is the injecting for the common man if that's creating a level of problem for the avid Nigerian and the very important as we are taught of I mean the idea might be entrusting on paper but in reality when you bring the policy and I try to execute the policy and you will be fine along the way but I am putting this to actualising the aims of the policy it should be the best part of the school.


My name is Sallianne Hart and I'm going to talk to you about the protective behaviours process, which is a process of empowerment and aims to enhance relationships. I also want to show you these little PB Buddies. A good friend of mine made these times when she's feeling a little bit unsettled, she should sit down and make a PB Buddy to remind us that in the protective behaviours process there are two themes, the two buttons on the head reminds of those and they are that we all have the right to feel safe all the time and that we can talk with someone about anything even if it feels awful or small. Protective behaviours is a process, it's a way of doing something and the way we do it is by using seven tools, so hence there are seven buttons in the middle of the body. The very first strategy is theme reinforcement. What is it I can do to reinforce these two themes? How can I demonstrate that my setting is a place where people feel safe and that they can talk? I talk about it as the scratch and sniff approach.  The second button in the protective behaviours strategy, the seven tool in the toolbox is about one step removed. Sometimes it doesn't feel safe enough to say how I'm feeling or what I'm thinking or to take responsibility for my behaviour. So I might say what if or I have a friend or how do you think our PB Buddy character is feeling? So we can practice things ahead of time and it helps us to hopefully feel safer because it gives us an element of control. The first strategy in the PB Toolbox is called network review. Who are those people I can talk with about absolutely anything, even if it feels awful or small and in protective behaviours. We would encourage people to have five network people and have different networks. So the little PB Buddy has got four networks here. One might be their family and friends network. One might be their professional network. One might be hobbies or a club network and who knows what other network might be. Some people have a religious network or a belief network. The fourth tool in the PB Toolbox is persistence. I think she definitely persists when she makes these. Sticking at something, stickability. That's a bit like resilience in protective behaviours. By resilience we don't mean stiff up a lip. We don't mean keep calm and carry on. We mean feeling safe enough to offer help for what you need. So persistent things. That's why babies are really good at protective behaviours because they persist. The fifth strategy is called protective interruption and that's about knowing when it's time to say enough now. Finished stop. My favourite version of that at the moment is a small child I know who now says I'd rather not as he's protective interruption. The sixth strategy is called risking on purpose because life is about adventures. To feel the fear and choose to do it because you want the outcome. The final button and I really like the one here. It's a big one. It's what sticks it all together. It's called the language of safety and it's about my communication and my communicating with people where I'm using quality interactions. Is there shared meaning in what I'm saying? Do my body language? Does that match what I'm saying? I'm hoping mine does now because I feel very passionate about protective behaviours. The final message is do I feel safe enough to own it? Oh my feelings? Who am I? Who am I? Sometimes I feel this. This is what I'm thinking and what are my choices? In protective behaviours we say that we can make decisions for ourselves but we don't need to make them by ourselves. So that's our little PvP pool, a person. We have a website called PvP pool which is a free community website. People can find all sorts of resources on there to help them feel empowered. Fantastic.