 Hi everyone, this is Chicho. Welcome to my channel and welcome to NutLiveStream. Today is April 23rd, 2020, and we're doing a drop in math tutoring session number six for the year 2020. Let's do some math and open discussion, and we've done a lot of these in the last couple of years. Basically, the name of the game is I'm making myself available for a couple of hours on a weekly, bi-weekly. We're doing two this week, one today and one tomorrow. So two to three times a month, sometimes four times a month, making myself available to help people out if they need any help in high school mathematics. But from that, welcome to our stream. If you want to know what we're doing, Mask of Raven, how are you doing? Oh boy, oh boy, you got your little wrench. You're ready for this, eh? Sausie, Rossie, how are you doing? Spider-Man, hello, hello, hello. I'm assuming the notification went out on Twitch, or not Twitch Discord, I hope so anyway. Nicholas, how are you doing? Welcome, welcome. Right now is a good time for you, Nicholas, it's evening, right? So that's not bad, nice chill evening, mass session. And for those of you who want to know who we are, I am posting everything on Patreon, so you can follow the work there. If you do have the funds, it's a great place to support this project. We are live streaming this on Twitch, and that's our Twitch channel. Yeah, 9.30pm in the UK, Connor Higgins, how are you doing? Welcome, welcome. We are live streaming this on Twitch, and if you want to catch these live, that's where you want to be at, and you can subscribe and follow on Twitch, so those are great ways to support this project, as well as stream labs, I guess, we have that set up as well. Simmer, how are you doing? I've always been making nice, nice nights of comic old, of old comics, old comics, how are you guys doing, man? I do announce these things about 30 minutes beforehand on Twitter, Gabs, Mines, VK, and Elo. Okay, there's a comment, no comics today, mathematics today, mathematics today, discordant, just went out, okay, awesome. Thanks, Spider-Man. Yeah, math today. There's a lot of people that need math help, really. My students, I have a few students that are in school trying to get their mathematics done, so I know the problems that people are facing. Liquid source, how are you doing? Welcome, welcome. Catholic traditionalist, how are you? Good afternoon, good folks. No comics today, nights of old comics, alright, but just having a glass of red wine. Nice, Simmer, very nice. We do math, we do math, and we do upload these videos on YouTube and Bichupe right now. Almost everything on YouTube so far, we're staying on top of it. Twitching Jason, how are you doing? And everything as long as it's processing on Bichupe. And we are times of pandemics, so if you want to flatten the curve, reduce the stress on your healthcare systems, then keep a little bit of physical distance and be aware of where you are and take care of people, right? That's the name of the game. Irrelevant of what you might have heard, the most important thing is to make sure your communities are not overwhelmed. And if there is something going around, right, indications are there probably is irrelevant of what you might have heard, then keep a little bit of physical distance. It's a good idea, right? Aside from that, welcome everyone. Hope you're doing well. Thank you so much. Spider-Man, you can't thank me. It's good, really. Thank you. Math time, Martin. We made buns on stream nights, what they kind of turned into biscuits. Biscuits are good too. Can the math relate to comics for sure? Nights of old comic. We did some, right? The last comic book reading we did was the price tag, the catalog order form that we got from 1968. That's what we narrowed it down to. So we actually looked at the prices that are now. So that was amazing. Amazing Spider-Man number 20 for a dollar, number 50 and number 45 for 50 cents. Now they're going for thousands, right? So that's pure mathematics. That's pure mathematics. It was brilliant. At some point we're going to take that. I'm going to include that in the whole series. That's part of my personal finance stuff. 100% guaranteed, man. I apologize for my abrupt things I said. Oh, no worries. I had an unexpected HR issue at work that I was called on. No worries, Catholic. Catholic traditionists, did you hear me sing Amy Grant? I don't know if she was your forte, but I did see her in concert. I don't know, how are you doing? Hello, everyone, that's Mask of Ravens. It says, mandatory face masks coming in the UK. Wow, wow, wow, mandatory face, yeah, some places are being hit hard, man. So those people that are saying it's all hoax is just because they don't see it where they are. It doesn't mean it doesn't exist in other places. It's like, that's weird. It's just, I don't get it. Mandatory face masks in the UK. Okay, the situation must be getting worse, I guess. I went for a walk yesterday. It was refreshing. I'm even in the rain. Nice. Yeah, the rain yesterday. Rain here as well. It was really good. I loved it. I went outside for a little bit just to take out the, what do you call it, recycling and compost. It was the day, right? And I saw people walking around in their rain jackets and stuff and it was nice. It just, rain has a sense of, by the way, Pacific Northwest, West Coast of Canada, United States in the border area, that's a rainforest. So we live in a, me and Hannah live in a rainforest. It's a temperate rainforest. So it does rain a lot here. On that front, it provides a lot of greenery. So there's a lot of green here, but we've been having a huge heat wave, sort of like forest fire season has already started where I am. So the rain yesterday was absolutely brilliant. Since we're about without Alex being next to my name, like on YouTube. Oh, Alex from YouTube. Alex Simmers. I go, man, there's so many names I'm trying to recognize on the switches between Twitch and YouTube. So it's totally throwing me off buying and selling, buying and selling Hannah. Any advice on how to make learning algebra easier for dyslexic people? Feed it to them faster. Knights of old comics. What I find is dyslexia. There's different. It's a spectrum, right? It's like autism. There's a spectrum. Everything is a spectrum. There's no absolutes, right? So it's a spectrum. So it's a fine balance, right? But for those who don't fit within the small box that our education system has created saying, okay, this is the way we're going to teach it and anyone that doesn't can't learn it in this way is, you know, they're special, whatever they call them, right? So they reduce the box smaller and smaller, right? Some people need certain things explained in a different way. Some people have little gaps here because of central education system stuff. But just because someone has is on whatever spectrum that they're on, it doesn't mean that they can't process certain information. Incredibly fast rates, right? They might have hiccups some places, but some of the other stuff they can process like speedy ones out style, right? Like crazy fast. Like seriously, I know because I've been doing this for 20 years, right? So you it's really important. That's where the decentralization comes in. If you have educators that are aware where the information blockage is, right? Then you can focus on that a little bit, help them through, but don't reduce the speed of everything else because there's different pipelines coming in. So that's one of the problems that people have with anyone that doesn't fit within the box. They slow everything down and that bores the crap out of anyone, right? Like really bores the crap out of anyone. I don't care where you're on the spectrum, right? So what you need to do is really pinpoint where the problem areas are. Work on those, but you can work on those as you're feeding on additional information. Layer it on so they see the whole picture, right? Once they see the whole picture, then it's money. As soon as that little blockage is fixed, like it's like a body, right? As soon as the muscles relax on one part, as long as you've been working out everything else, it just fits into gear, right? It just goes into place and everything works together brilliantly. It takes time, energy, effort, patience, kindness, frustration. It takes all that stuff. But front load and the work, put the work that's needed at the beginning of the stages of educating anyone in any subject and you reap the rewards towards the end, right? That's my advice. Take it as you wish. Prophet and Spiderman 442, yeah, 4118% profit. That's sweet money. Wow, that's really, I must have through that rant, I must have. I did hear that. I pronounced half that stuff wrong. Actually more than half, probably all of it. I'm going to scroll down again, because I know off my rant, I missed a lot of chat. Odmek, how are you doing? Hello, hello, honestly, Pacific Northwest sounds like a dream climate. Doing calculus today, no calculus today. I've been really busy doing a lot of things. So I'm not going to touch up on my calculus, Odmek, until the summer. I had an influx and more requests to do online teaching with some of my students and I picked up a couple of extra ones and stuff. So I've been really trying to make sure I can fit everyone in because if any of my students have a hard time, they come first, right? I fit them in wherever I have time available. So hopefully this summer, I'll be able to pick it up. Hello, how are you doing? How would you solve LawnX? Let me write this down. That's the first math I saw. Let's check it out. LawnX. We don't need to put it in brackets, but whatever. Where'd it go? Oh, I lost it. The chat. Oh, no, there it is. Minus 3 square root of LawnX minus 3 square root of LawnX plus 2 plus 2 is equal to 0. You sure that's not squared? Oh, no, it doesn't need to be squared. Does it? No, it doesn't need to be squared. How would we solve it? Is this x under the square root? Yeah, it is. So the way we would do it, do it this way. Okay, let me scroll down. So this is number one. Let's deal with this first. I'm missing a lot. How are you doing? Welcome, welcome. I'm going to scroll down. That way, if I make any mistakes in this, people can correct me. Right? What does a house wear? Vivian, I don't know. House wear sightings. Chichana, I have a small problem. I bought a small portable charcoal grill, and I want to start grilling more fresh meat. Through quarantine, I'm staying at my Gopher's studio where I can, where can I grill it on the roof, I guess, in the empty part? Sure, wherever you can find. But I'm going to scroll down, Hannah. There we go. Can you explain plank length in math? Not not the mathematics of it, but I can explain the concept of it. Right? Yeah, that's exactly the mask of Raven. Mention that. That's exactly what we're going to do. Square root as you would do this. So for example, take a look at this. This is long to the power of one of x minus three long x to the power of here. Let me do it in a way where it's obvious. This is to the power of one. And this is to the power of a half plus two is equal to zero. Right? That's what it is. And a quadratic function is this x squared here, a x squared plus bx plus c is equal to zero. Right? So this is a quadratic function, and we can factor quadratic functions. Right? So for example, just imagine you had this, right? Just imagine a was one. So let's set a is one, b is equal to negative three, and c is equal to two. Okay, so just imagine a is one, b is negative three, c is two. Right? So what we have now is one x squared, which is just x squared plus b not b. Negative three. Negative three x plus two is equal to zero. Right? Take a look at this. So that's our negative three. There's a one. There's two. Right? So let x or you as a mask of ribbon said let's say you let's set you let's set you you equal to lawn square root of lawn and right. So let you equal the square root of lawn x. Yeah, it has to be x. Sorry, I didn't realize. I forgot we use the next already. So I'm gonna use the next year. Right? Actually, I should call these ones you too. Right? My bad. Use the correct terminology. You you mask of Raven as a head of me on this one. Right? So you're gonna let this equal this, right? So that's really that guy. So all we got to do is factor this guy. Right? Because if we sub this in for this, this is exactly what we're going to get. Watch this, we're going to get squared of lawn x squared minus three squared of lawn x plus two is equal to zero, which is our original question, because squared of lawn x is just lawn x, right? Because they kill each other. Right? As you know, x squared of x is x to a power of a half. So if you have squared of you squared, that's going to be you squared to a power of a half, which is just going to be you, which is what we got. Or anyway, you get the gist. I'm using the wrong letters. I'm reusing them. It's just not the best thing to do. But this is what happens when you look at Chad and look at the screen and look at this. Right? So all we got to do really is just factor this. So let's just factor that. Right? So let's kill this guy. Factor this guy. Two numbers that multiply to give you positive two, add to give you negative three. Okay? Negative two times negative one. Right? So you're going to get you minus one, you plus minus minus minus two. Because if you foil this out, you're going to get you squared minus two you minus you plus two. Right? This is just straight factor. So now what you can do is just say you minus one is equal to zero, you minus two is equal to zero. So you is equal to one and you is equal to two. Well, what's you? You is well right here, you is long x. Right? So what you can do is go let's go. Can you see where this for now? Yeah, you can see this for now. So now what you do you say, square root of long x is equal to one and square root of long x is equal to two. Well, long x long long of something is log base e of that thing. Right? I think so. I hope so. This is for statistics, yes. Is it for statistics? Like, no, this is this would be quadratics and logarithms. Right? Let me make sure I'm going to reach out and make sure I didn't make any mistakes hardcore. That's a strange formulation for that equation. What is there to explain? While solving it, right and what how you can do it is called substitution. Right? Thanks, guys. The person with dyslexia is me and I stopped that algebra. Okay, algebra, because I just couldn't process it. That was in the 80s. And no one even thought of dyslexia. So I was left with the belief of I'm not smart enough for that. Yeah, Knights of Older, Knights of Old Comic, there's lots of people that have come across even now, right? But I started working with it like, what? You like, all of a sudden they understand something that they never thought they could understand, which is just because it was just shown, you know, they're having the attention that someone really focusing in on the problem and feeding that little just putting that little brick in the right place for them to move on. It's unfortunate. It's just a centralized system. We can't handle unique people, right? Unique ways of being right. Otherwise, I'm older now. I'm sure you can learn. Yeah, school failed you, not the other way around 100% on that's exactly what it is. Need a scroll command. Oh, maybe. Yeah, yeah, scroll command. This is that. Okay. No, this is a log problem. Yeah, it'll be log problems. How's it going? You just doing well, Quinn? How are you doing? Okay, so basically it's this. So what we got really here is we can see it. So this is really log e of x is equal to one and log e of x is equal to two. Oh, sorry, I forgot. I forgot to square this. This is squared. This is squared. So that's one squared is one and this is squared. So this is four. Right? You need to get rid of the square root, right? Class is essentially how's it going? Okay, so let me go back here. I'm going to kill this guy. Okay, I'm going to continue to work here, because that was just redundant. That was just this. Right? So right now we have this log e of x is equal to one and log e of x is equal to four. Right? We had long squared of long x is equal to two, you square both sides, you get four. So there's the rule that says you can kick this up. Right? And then these guys go up and this is logs. I'm not covering the logs aspect of it, right? This is just one of the things you can do. So one of the log rules. So x is equal to e to the power of one and x is equal to e to the power of four. Does that make sense? Does that help you out? I forget who it was that asked that question. Oh, it's way up there. So I'm not going to scroll way up trying to find it. Thanks, Admin. And this is about this lecture. I hope to try again, so I can help my daughter by the time she's learning algebra and beyond. A nice old comic, you should begin now. I don't know how old your daughter is, but you need to begin now. Okay, when I started teaching mathematics is when I really started to understand mathematics. I didn't know it beforehand. I made a lot of mistakes. I don't I don't know if it was mistakes. Like, I don't I didn't explain things as well as I do now, as I did during the first three, four years of me teaching five years of me teaching because I didn't know math. I had students come up to me and say, Hey, why do you do this? I'm like, I don't know, I just did it. I just know how to do it. Right? What's the core reason why I do this? I didn't know. Right? And then I would read, I would read, I would watch videos, I would do this. I mean, well, back then, there wasn't that many videos. It was, I was using soul seek back back then, three computers uploading, downloading. So I was grabbing a lot of anything I could find, right? So I would do my research and learn it. It was hard work, man, learning math, learning how to teach high school mathematics, elementary school math, difficult. Seriously, it was very challenging. I highly recommend doing it. You're better for it. Very powerful stuff, Chicho. And the mirror, you were able to solve a law problem by using a completely different idea, which is quadratic. There's a lot of beauty to this problem. Yeah, for sure. And this is how else would I solve this? I mean, this is basically my to go to method of doing it. I can't think of another way. Quinn, thank you very much for your one sub two months in a row. Where were you during my college days? Oh, and hello, lark bark. How are you doing? Math is relative. Hey, math is relative. Math is relative. Math is pretty absolute, actually. The how you apply mathematics, people's understanding of mathematics, different disciplines, the different level of mathematics they use at different disciplines is all relative. But mathematics is pretty pure. How you use the language is relative, right? But the language itself is not verbal languages are more associative relative descriptive than mathematics. Other I'm gonna bite my tongue on that one, because math really describes everything without the I don't know, it's different. It's different. I was gonna say without the emotional attachment, but there is amazing beauty and emotion associated with mathematics without the biases. To a certain degree, I would say without the biases. Knights of Old comic, Audmik says your daughter might be dyslexic to she's lucky to have someone so special and understanding to help her out. Yeah. Really? Like one of the reasons I'm able to work with a lot of people that don't fit inside the box is because I didn't fit inside the box. Like really, you should have seen me pounding against the walls of the box. But and the box when I was growing up was a lot bigger than the boxes. Now the box is way tighter now. Right? So I feel for a lot of kids that trying to go through the system horrendous, horrendous, right? Brutal, brutal. I was joking that equals MC squared is not really Oh, equals MC squared. Yeah. Are you on real analysis? How are you on real? I'm not sure what real analysis means always be making. What do you mean with real analysis? I need an example. I don't know what the words mean. The different disciplines, a lot of problems. They're quite different from regular problems. To a certain degree, they have asymptotes, right? Yeah, math was pure and only until all Mr. incompetence theorem came around. Curved Google. Incompleteness theorem. You can't, you can't say that anything is a pure system from inside the box, unless you step outside the box, the incompleteness theorem, right? Google, that's why he went crazy, odd Nick, right? Trying to figure out infinity matrices are also awesome. It's like a different way to do math. And it works and it works. Yeah, I got a brush up on my major and relearn it anyway. I'm doing great. Thank you, Lark. I'm doing great. Thank you. And I could have used this tutor tutoring during my college years, although I must say I got much, I got much with my math during my college days. Nice. Rickety Rocket. Hello, have a question for you. If you're running in a race, and you pass the person in second place, what place are you in? You passed the person in second place, your second place, right? defining the real numbers. defining the real I like real, not the real number set one of the first videos I think video number three I ever put out for one of the third video I ever put out regarding mathematics was the real number set. Oh, doing some calculus. I just finished this class had a lot of fun. Nice. That's what I like to hear fun with mathematics, right? My parents work in the system, both being teachers, and I hear the frustration about stuff like that all the time. Yeah, Quinn, incompleteness doesn't necessarily take away the purity for me. Mask of Ramesses to Omnic. I've noticed the two underdog comics, comic books in the background as well. Yeah. Well, one is underdog the almost Mickey Mouse. Mighty Mouse, right? Mighty Mouse. Mighty Mouse is awesome. Real analysis is a formalized formalized calculus with proofs. Then nope, I'm not real analysis. I'm not good at anything involving proofs. In general, I'm not good at my mind functions more on solving than proving it's a branch of math. It deals with limits, continuity, series sequences, differentiability. I like limit I like limits and I like graphing functions. So there might be parts with it like, I like it too. Mask of Ramon, you like it. I think it makes things much more interesting. Or the incompleteness theorem. Yeah, yeah. Who was publishing the underdog It was at the underdog comics was Charlton comics. Charlton comics. And this is number number one. I think it's the first time you appeared on in comic books. Rickety Rocket, thank you. That is correct. So my people get it wrong. It's disappointing. It's it's a trick, right? Absurd icon. Hello. Hello. How are you doing? I love how you solve problems. If I may, how would you solve the problem? That's a log problem. Here, here's the rule for the log. Let's stick with the logs. I like this. Let's do mathematics. I like logs. I love logs. Okay, so how do we do this? So what's what are the log rules we have? Right? There's some core log rules we have like 10 of them, right? So let me write down the problem. So I don't lose it. Lawn x plus Lawn is equal to x plus two is equal to four. Right? What are some of the long rules that you have? Right? Think about the long rules rule you have. And which one applies here? Okay. And and no mirror. Okay. Mathematics absurdicon. I'm going to scroll down a little bit. Absurdicon. Just so. Yeah. Absurdicon. Yeah. Yes. Absurdicons. Absurdicons got it, by the way. Right? Okay, great. Thank you for your comic knowledge. Well, I just looked at it. What it is the first one. Product rule. If I'm correct. Exactly. So basically you drop the next. Don't drop the next absurdicon. So one of the rules is if you got log A plus log B, then this is equal to log A times B. Right? And that's this guy. We got log of something plus log of something. So that means it's equal to here I should write it down downwards. I don't like going sideways on on. Well, it is identities. No, let's do it. Log A B. When I'm solving, I don't go sideways. Right? So this is really this. So all you would do is just go log. Oops, I was going to put it as a fraction as a division. The division would be divided by right. If this was a minus that this would be log A divided by B. Right? So this would be log x times x plus two is equal to four. This is lawn. So lawn is log to the base e, kick the e up, kick the four up, multiply this out. So you got x squared plus two x is equal to e to the power of four, and then kick that over plus two x minus e to the power of four is equal to zero. And from here, you just use the quadratic form. Let's solve it. Mine says that's gangster. Nice. I remember watching an old stream and you're all dealing with the dial fencing equations. I think it was about counting how many cards with so many passes. My favorite part of math are the pure concepts like metric systems, density, completeness, continuity, mask of raven. But by the way, Audnick, mask of raven, have you guys seen the or anyone that likes math? Have you guys ever seen that documentary called it's either forbidden knowledge where it's a documentary about this mathematician that made a documentary about his three of his favorite mathematicians? One of them was Google. I don't know who the other, I forget who the other two are, but they're huge mathematicians. And they went, one of them went insane. No, one of them killed himself and two of them went insane thinking about infinity. I don't know. You guys are smart. I don't know if smart is the right word. It's just that this is just knowing mathematics. It's just a rule. That's it. I'm a web dev going back to school for CS. Haven't done math in years. Teach me. Cipher, McKay. What are you going back for? Computer science. You need calculus for computer science. You need statistics for computer science. What else do you need for computer science? You need pre-calc. You need to know logs, exponential growth. You need to know a lot of stuff. Maybe not smart. You can get pretty far with enthusiasm, on make well put. So on makes response to, you know, while you guys respond to a math, on makes responses, what should be, what I should have said, which on makes says, which is maybe not smart. You can get pretty far with this enthusiasm. Right? Which is fantastic. An anger. How are you doing? Very Lovecraftian. The pursuit of knowledge leading to madness. Yeah. Raman Dhan did a lot with the constant infinity. If I recall correctly, I don't, I forget the names. Kulio, how's it going? Maybe they didn't go insane. Maybe they learned the truth and the gods of math had to summon them to impart their knowledge and the superior, maybe. Right? Infinity used to trip me out as a kid. Yeah. I didn't really understand the concept of infinity until way after. I don't even know when all of a sudden clicked, right? It just went, oh, wait a second. Raman Nujan. Raman Nujan was his name. Okay. Hey, first time here. Why are we doing logarithms? Because someone asked the question about logs. If you have a math question, we'll take a look at it, right? I got new pens and an eraser. Olive, how are you doing? How's life, Olive? I've lately been of the thought that we should introduce infinity in math early, seeing as many kids seem to gravitate towards thinking of it and it's kind of fun as opposed to just memorization stuff. Mask of Raven, 100% agree. 100% agree. And I do do it with some of my younger students when we start talking about counting, even the real number set. I start planting seeds regarding infinity and whatnot. Autnexus, Chichu, diaphantine equations are neat because if you guys accidentally did number three, because you guys accidentally did number three, the question was something about if you have three players run out of cards after x many passes, it's a pretty big field of research. Oh, really? I think I remember the question that we did. It was a very nice, clean way of solving it, I believe. I was having a hard time wrapping my head around it. I think Mask of Raven was trying to explain it to all and then all of a sudden when I saw it I thought it was like, oh wow. Oh, derivatives. I don't like derivatives. Not yet. I'm not good at them right now. Sorry, odd making Mask of Raven might be able to do. By the way, as snacks today, Olive Life is good, but I should go to sleep. Have a fun stream. Good night. Good night, Olive. Thanks for popping in. I think the easiest way to introduce infinity kids is to use the equals one. The easiest way I do it, I just tell them, here, imagine this. For me, there's two things I say. For me, there's two definitions of infinity I use. One of them is something that goes on forever and the other one is the universe explodes. So I tell my students, I go, okay, look, think of infinity as two different ways. One of them, just imagine yourself counting forever. You can imagine that, right? They go, yeah, yeah, I just count. Go up. And then I go, the other one is the universe explodes. Chips. Sometimes you just got to eat chips, man. Really. Honey Dijon. And I use, uh, check this out. And I usually just use yogurt. If I ever use dip, I just use straight yogurt. Right? And yogurt and chips. These chips are really good. Oh, nice. Catholic tradition does it. The dip in it, it's phenomenal. It balances out the saltiness. Derivatives are more fun when you learn the tricks to calculate them quickly. Yeah. Then it's just algebra, meditative. Very true. Same with ODEs. That's the derivative of that. Yeah, masquerade, cool. Catholic tradition does it as well. Nice, nice. Yeah, that's it. Surdukan. Nice. I also feel like most kids confuse infinity with an actual number. Yeah. They don't realize it's like a limit, right? I know. I did when I, I did too. Amirio. I did as well. It's an identity if I'm correct, correct, or something along those lines. Identity. I think of it as a limit. I don't know if that's the right way of thinking about it or not, to be true. I like that example. If you want to confuse them further with quantum physics, they can count to infinity while the universe explodes simultaneously. Cool, Leo. I'm going to start using that. Well, I'm going to read this again. So there's two types of infinity. One count to forever. Yeah, you can imagine that or universe explodes. And if you want to teach them about quantum physics, you say, if you want to confuse them further, you say, oh, do you know what quantum physics is? You would say, well, just imagine you counting to infinity while the universe explodes simultaneously. So that's what we're going to remember. Just imagine you counting to infinity while the universe explodes simultaneously. Oh, I'm going to try to put that to memory. Cool, Leo. Sorry, Mr. Traditionless. Mom, see you there. Nice two answers confirmed, right? Why not? What kind of yogurt? Just straight up yogurt. Usually I grab 3%, but when I went to the store a few days ago, 2% and 3% was gone. So they either had Greek yogurt, which is like 6.5%, the one that I get, and grass-fed Greek yogurt, or they had 0%, right? So I like 3%. So I took the 6.5%, I bought 6.5%, I bought 0%, I put them together. So this is 0% and 6.5%, 6.5% mixed together. Addictive. One more. Sounds like a Thanos quote. Martin says, okay, we've got another math problem. Let's check it out. Love them, hate them at the same time. Complex analysis is very cool. It's just, it just seems like such coincidence, residue integration, and such actually works, provided sufficiently well behaved functions. Let's check this one already raised up nice. 5 brackets, negative 3x squared minus 2. Was this squared? No. Minus x minus 3, minus x minus 3 equals negative 4x plus 5 plus 13. This isn't even, there's no squares here on a white board. What do we get? Let's see if it works. Well, it should work. Got to love that e to the power of i pi is equal to negative 1. Just multiply everything up. This is, whenever you see a negative in front of bracket, it's a negative 1. You're multiplying the negative in. If it's a positive, you don't need to do anything. You just drop the brackets. If it's a negative, this negative goes in. Right? Here's a negative 4. Always remember the sign in front of the number goes with the number. That should be like a mantra. Sign in front of the number goes with the number. Sign in front of the number goes with the number. The other one is, reduce before you multiply. Reduce before you multiply. Line up your equal sign. Oops, equals upside down. Don't line up your equal sign like that. Line up your equal sign. Put it in the middle. Multiply this out. So negative 15x minus 10 minus x plus 3. Multiply this out. Negative 16x minus 20 plus 13. Before you move things around, combine your like terms on either side first. Line up your equal sign. Right? Combine your like terms. This guy adds to this guy. So it's negative 16x minus 7. This guy adds to this guy. This guy adds to this guy. When you're looking at expressions like this or equations like this, circle things, box things, underlying things, so you see visually what needs to combine with what. Right? It makes life a lot easier. So you got negative 14x minus 7. Right? Oh, negative 16x minus 7. So what do we have here? We got 0 equals 0. 0 equals 0. Right? That's what you got. It's the same thing, right? You bring this over. Plus, do this right? Yeah. Plus 16x. Bring this over. Plus 7. 0 equals 0. x equals 0. Does x equals 0? Here, let's do a test. Do a test run on this thing. Because we didn't get x is equal to 0. We got 0 equals 0. 0. Right? So anything. So it's the same expression on both sides as Racer Kill says. Right? So it doesn't make a difference what you plug in. Right? Take a look at this. We got here. Let me rewrite it. Negative 16x minus 7 is equal to negative 16x minus 7. It doesn't like, it's the same expression. This is exactly same as this. So whatever you plug in here, you got to plug in here. So they're both equal. So it's just the same thing. Right? Yeah. Negative 16 boxes minus 7 is equal to negative 16 boxes minus 7. What can you put in the box to make this equation true? Anything you want because they're the same thing. This is this. x is just a placeholder. Right? Anything you want. Here, let's put a function in here. Let's in the box, let's put ln x minus 2 over square root of x, y plus 7 cube minus x plus 3. So let's put that in here. Well, that's the same. Put it in there. So it's true for that. Whatever that is. I don't know. We can put numbers here. 10, 5, 2, whatever it is. Irrelevant. Solving an equation means finding every solution. In this case, every number is a solution. Where are you from? I got to ask you, Joe. Lark, I live in the west coast of Canada. West coast Canadian mainly, basically. Okay. Born in Iran, Armenian ancestry. So my first language was Romanian. My second language was Farsi. My language that I can read and write, that the only language I can read and write and speak way better than any of the other ones is English. What if you put the Schlosser's cat in the box? Oh, I saw something, a little cartoon thing. Where, oh, I forget what it is. Some mathematician is giving a present. I think the cartoon was, where did I see this? The cartoon was a mathematician is giving, giving a... box. So this is the mathematician, right? He's giving a box, a present, I guess to his daughter, right? And the mathematician's partner is saying, I hope it's not another dead cat in the box. Where did I see this? I don't know where I saw it. It cracked me up. It was so funny. It was so funny. So funny. Canadian people. I'm Canadian, yeah. For sure. I'm pretty sure those Canadians here, for sure. Just turned in after no school for a mom on that question. Just frazzled my brain. British here, British. You're welcome, Lark. Porsche Schlosser, his cat is so often misinterpreted. So geometrically, the two linears are... Yeah, they're two here. Let me show it to you. Watch this. So we have... What was it? It was negative 16x minus 7 is equal to negative 16x minus 7. Let's call this y1. Let's call this y2. So y1 is equal to negative 16x minus 7, and y2 is equal to negative 16x minus 7. And then the question would be, solve this linear system equations. So solve this linear system equations, blah, blah, blah. So you could do it with substitution elimination. You could do it graphically. Let's do it graphically. Graphically, negative 7, 1, 2, 3, 4, 5, 6, 7. The slope is negative 16 over 1. Ah, pooper, scooper, right? Instead of going down 16 and over this way 1, I'm going to go up 16 and over this way 1. Because negative... Yeah, negative... Up positive, negative this way, right? So that was 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, and then over 1. So here's our graph of y1. This is y1. That's graph y2. Graph of y2. What? Same thing. So this is an infinite number of solutions. The two lines are on top of each other. Me too. I'm Armenian, but my native language is Russian. Nice process. He was pointing out the absurdism of the many worlds interpretation. Odmek, by the way, have you seen Devs? The TV show called Devs? Have you guys, has anyone watched the TV show called Devs? Okay, can we whiteboard this one? 1 over... Yeah, sure. Let's do it. That's a quadratic with minutes or restrictions, right? So 1 over m plus 3 plus 1... Oh, that. 1 over m plus 3, 1 over... Okay, so we got this. 1 over m plus 3 minus 1 over m plus... Minus? Minus. You're switching. Yeah, you're switching them. And it was a plus. I got that one wrong. So that's a plus and that's a minus. Minus 3 is equal to 1 over m squared minus 9, I believe. Isn't it? It should be 6. 6. Do I have the numbers right? Yeah, are you familiar with trig identities? Yeah, I usually have to look at the formula sheet, but the half of them for sure. Love Devs. Yeah, it was great, eh? Great series. Oh, Racer kills on it. Nice, nice. Nice. I haven't seen Devs. My friend recommends it, but I'm staying away until it's over. It's over. It finished a couple of days ago. Worth watching. Good evening or good morning, good morning, or good afternoon for my end. I need to do some stuff and sleep. Okay, Chicho. Devs is made by Alex Garland. If you'd like the show, check out Inniolation and X Machine. Oh, X Machine, I know. X Machine, I have read a couple of the trades. It's really good. Inniolation, I've read. Inniolation, Odmic. Inniolation was, we're talking about comic books, right? Multiple to first with that. Is it a mini series or will it have another series? I think it's done. I think Devs is done one season as far as I know. I will start watching Devs tomorrow. Nice. For this one, right? This is just factoring stuff. So we don't need the brackets here, by the way. Unnecessary. And we don't need the brackets here either. It's unnecessary, right? Inniolation are both movies as well, I think. Oh, I didn't realize X Machine was a movie as well. I wish you were my math teacher. I'm here making myself available two hours as often as I can. We're doing one today. We're doing one tomorrow, two hours. Go review your math if you have problems anywhere. Come back either today. We're here for another hour or tomorrow, right? You're going to run into zero in the denominator. Yeah, you've got to do your restrictions, right? X Machine is a great movie. Oh, what? I've got to watch it. Wait a second. X Machine. Oh, wait a second. I've seen X Machine. It's AI. It's the girl that they're making in the secluded place that's AI, right? She gets awareness. A real life math. I tutor privately, yeah. I teach privately, and I work with some schools to teach some of their kids. Inniolation is based off of a book series called Southern Reach Trilogy. Natalie Portman is the main character. Real trippy, confusing movie. Oh, I don't know this one. It doesn't get a lot of love, but probably my favorite film in the last five. Oh, Autmic. Can you post it in our Discord folder? I appreciate that. And X Machine, I think it's Natalie Portman as well, right? She's the AI. Yeah, that's right. AI, Android, that gains awareness. Yeah, that was a good movie. I liked it. That doesn't get any love. Oh, no. Inniolation doesn't get much love. And inniolation, that's the one they go through a portal into another world, right? Another time zone. And then it's... Yeah, it's like same thing as our place, but there's like different creatures in there and stuff, right? Yeah. That's a great movie. That was a really good movie. What? Yeah, I've seen both of them. Oh, that's why. Yeah, I've seen both of them. That's right. It had a very same, similar feel to it. Yeah, yeah. They're both really good movies. I like them. And X Machine, there's a comic book series called X Machine, but it's totally different. Yeah, yeah. Great movies. I didn't know that. I didn't know that. You'll love it. You'll love that. It was really good. Fun movie. Okay. For this one, you just got to factor this guy. If you factor this guy, it's the difference of squares, right? M plus 3, M minus 3. That's that guy. Kill it. You don't need it, right? You don't need... I mean, HP, HP is... Inniolation has tons of similarities to color out of space. I don't know color out of space. Oh, okay, okay. So take a look at this. Whenever you're trying to solve for any mathematical equation, any mathematical equation or function, color out of a Nicholas Cage film, what? Color out of a Nicholas Cage. Some Nicholas Cage films, amazing. Some of them. Oh my God, right? He must have had to pay some bills, right? Came out late last year, I think. Oh, really? Cool. Based on HP Lovecraft. Oh, very good. This one is supposed to be really good. I need to watch it. Oh, I don't know this one either. If someone remembers, please post that in the full section of 2 seconds. I can remember to watch it. Color out of space. So first thing you do, whenever you're doing any math problem, any math equation, any math function, whatever it is, you find your restrictions. What can't we do in mathematics? Divide by zero. So whenever you see a denominator, if there's a variable in there, you grab it, you say that can't equal zero. So usually I do it on the side, but we have no space, so we're going to do it on the bottom. So this M plus 3 cannot equal zero. This M minus 3 cannot equal zero. This M plus 3, M minus 3 cannot equal zero. M cannot equal negative 3. M cannot equal 3. And this is M plus 3 can't equal zero. M minus 3 can't equal zero, which is the same thing as this. M can't equal negative 3. M can't equal 3, which is the same as this. So we don't need this. This is redundant. It's the same deal. So these are restrictions. And then you can start solving it. So one thing you want to do when you're solving these types of equations, you want to get rid of the denominator, simplify life. So to get rid of the denominators, you're on an equal sign. As long as you have an equal sign, it means you can do anything on this side as long as you do it to the other side. So we're going to multiply the whole equation by the common denominator. What is the common denominator? The common denominator is M plus 3 times M minus 3. Multiply the whole equation every term by M plus 3, M minus 3. She chose a great video on Arrival. Oh, Arrival, yeah. That was a good movie. I like that. This would be just solving rational functions, rational equations. So this would be grade 10, grade 11 in my naked words. So this guy multiplies this, multiplies this, and multiplies this. What happens when this multiplies this? Well, M plus 3 kills M plus 3. So it's just M minus 3. Plus, what happens when this multiplies this? M minus 3 kills M minus 3. Oh, yeah, minus 3. So it's M plus 3. I hope that's clear. Do we usually stay around this? No, we go all over the place. I'm not really touching calculus. We did a little intro to calculus last week or the week before on a previous set. I think it was last week. And we do a little bit of stats. Do you do any higher level calc or optimization problems? Steadying deep learning on my own time. No real human being. Humans being. You must being. No, I'm not doing that right now. I'm not doing hardcore calculus. Just this stream we've done. 9 minus 2 in terms of subject matter. 9 to 12 in terms of subject matter. Yeah, hopefully it wasn't 9 minus 2. We're not doing 9 minus 2 for an hour. Which equals, what's this times this? Well, these guys kill those guys. So that's 6. So right now we got 2M is equal to 6. This kills that. Divide by 2. So M is equal to 3. That's your answer, right? That's your answer. But you got to check your restriction. M can't equal 3. So there's no solution. Okay. So we got to check your answer. That's your restriction. No solution. Can't do it. Has anyone seen the film Pie written them? Yeah, for sure. It was a good movie. Fun movie. That's a lot of things. I'll give a follow anyway. I might be a bit rusty on this stuff. This stuff is pretty important actually. This is the core of calculus. Right? Oh, that's why you're going to stick around. Yeah, you need to know this stuff 100%. It's never been a bad idea to practice earlier stuff. Yeah. Yes. Negative 3 subject matter. What does this mean graphically? What does this mean graphically? Well, let's graph it here. Let me show you what this means graphically. Well, I'll show you what one of the functions looks like. Let's graph this guy. Okay. Which is the same as this guy. They're both the same, right? So let's just graph this. Let's assume you have the following function. Right? Let me just get caught up with chat a little bit. All right. Let me write it down. So we're going to graph this. f of x is equal to 6 over m squared minus 9. Yes, pie is also fun. Amazing micro budget film. Amazing micro budget film. I like those. And primer. Primer was another one which was really good on the same level as pie. Do you know arithmetic algebra rules for equations with probabilities? For example, probability of x greater than 4 equals probability of x less than 2 plus a half. No, I haven't dice power. I haven't gone there yet. I've worked with some students. I have one student this year that was doing a little bit of stats. I would work with a little bit, but I'm not comfortable enough to teach it because I don't, yeah, I'm not comfortable enough to teach it just to put simply, right? When people start doing operations for normalized variables, etc., I never know the rules for how the outer equation and inner inequalities interact. Wait, what? I got m equals 6. Did you cipher it? Did I do it wrong? You have to divide by 2. You have 2 m is equal to 6, right? These two graphs never need. Can we do something simpler, like 10 plus 12? 10 plus 12? Yeah, 10 plus 12. 10 plus 12. Lay them up vertically. 10 plus 12. Add each digits. 2, 2, right? Let's assume you had 9 plus 18, and let's make this 8 and 3, right? So we got 98 plus 83, right? Let's then want to get my eraser, but I have to grab my eraser. 8 plus 3 is 11. You put the one here because it's 11, it's a 10. You carry it over. You put one on top of your 9 plus, 1 plus 9 is 10, plus 8 is 18. Straight up, right? No, wait, see the error. Do you like beard? Marsh, Marshman. I like gothies right now. Gothies are awesome, and I do like beers. Just do Chicho Beards. We have a beard playlist on YouTube. M equals 3, but 3 is excluded because it deals 0 on the denominator, so no solution. You ever heard of Andrew Gilman? Great statistician. I'm reading his book right now on Bayesian stats. No, I don't know. I don't know. You would see the two graphs get very, very close, around 3 and negative 3, but never meet. Infinitely close. Beard, is it? Bread. Oh, bread, not beard. Yeah, I love bread. I love Beards. Thanks for that. I read it all wacko. This is Chicho reading words and names and stuff. Is it a classic text word? Bayesian data analysis, Catholic tradition. That's cool. That's cool. Yeah, that's close as you want. Yeah, Catholicism. Observe. Absolute class. Is it absolute classic? Really? Unless I'm missing something major. What's more random equation tomorrow? I watch math films starting with under the heavy topics. Okay, take a look at this. Let's graph this guy. So if you're graphing a function, first thing you got to do is the same thing you did when you solved an equation. Find your restrictions. What are your restrictions? Well, the denominator can't equal zero. So let's do the restrictions here. Restrictions. And usually when I'm doing graphing functions, solving equations, you go to one side and you say restriction, and you know this is your restriction for either your equation you're solving for or your problem you're solving for or your function you're trying to graph. So the denominator can't equal zero. M squared minus nine cannot equal zero. M minus three times M plus three cannot equal zero. So M minus three cannot equal zero. M plus three cannot equal zero. So M cannot equal three and M cannot equal negative three. That's your restriction. Your restrictions can either possibly be holes in your graph or asymptotes in your graph. So as soon as you find your restrictions factor, simplify your function. So this becomes six over M plus three M minus three because we factored it. That's what it is. You want it in this form. So as soon as you have that, you're ready to graph it. Now if you simplify it and one of the bottom guys cancels, one of the restrictions cancels, is no longer an asymptote, it's a hole. But since nothing canceled, we have two asymptotes. Our asymptotes are M equals three and M equals negative three. And this is my bad, my terminology. This should be an M. It's not f of x anymore, it's f of M. It's just like saying f of x and these would be x's. And x is M is our x axis. So your asymptote is your restriction. M equals three and M equals negative three. So draw your graph. Your asymptotes one, two, three, one, two, three. Or your asymptotes are M is three, which is a vertical line, and M is negative three, which is a vertical line. So here's your asymptotes. That's negative three, that's three. Now what you need to do is graph it. That's all really. So you can just test points to be able to graph this, or you can go, hey, this is, if you're going to graph this, that's really a parabola with the vertex being at negative nine and zero. Now this is symmetrical. So what you can do is find different points on here. And by the way, these are your vertical asymptotes. You also have a horizontal asymptote. Let me give you the rule for the horizontal asymptotes. Let me erase this. Hold on, let me put it over here because we're going to need the space down. I scaled it that way, unfortunately. So asymptotes, asymptotes is M equals three and M is equal to negative three. Now your horizontal asymptotes, for any rational function like this, this is the rule that you need to remember. Okay. If f of x is equal to, let me put this in a box, is equal to A x to the power of n plus dot dot dot over B x to the power of m plus dot dot dot. Right. Any polynomial function on top of another polynomial function? Okay. Your asymptotes are this. If M equals n, then your horizontal asymptotes, f of x is equal to A over B. If M is greater than n, then your horizontal asymptote is equal to zero. If the power in the bottom is bigger than the power up top, then your horizontal asymptote is the x-axis. If M is less than n, which means, I should have written this as, uh, wrote these the other way, right? Yeah. Anyway, because n is a higher letter than M, right? So you would assume n is usually higher. I'm trying to make it symmetrical, but it's okay. So if M, if the lower power is smaller than the upper power, no horizontal asymptote, no horizontal asymptote. So what we have here, the bottom power is higher than the top power. So we have f of x is equal to zero. That means your x-axis is also an asymptote, right? So we found our boundaries. We've got six zones, this, this, this, this, this, this. Now we need to find out where the function is, right? These are essentially, uh, cancels. So not an asymptote. It means there were on top, then top and bottom would cancel. Yeah, the top and bottom. I can show you here, if you had, for example, let's assume you had this M minus three up here, M minus three up here, then the M minus three would kill the M minus three. So your final reduced format of this would be six over M plus three, right? So M minus three would be an asymptote, but there would be a hole along this. This asymptote would not exist, okay? So all you would do is put a substitute, find out, find out what f of three would be. You plug it in. It would be one. So there would be a hole at y equals one. X is equal to three, y equals one would be a hole. We can graph it after this. We'll graph it after this actually so you see the difference. Let me erase this for now and we'll add that addition in there. Okay, let me scroll down, make sure I didn't make any mistakes. Why don't you just use Dorotis? Because I'm not doing calculus, and I like doing it this way to tell the truth right now, because I'm not doing calculus. Are you a teacher? I do private teaching, yeah. I do private math teaching for sure. Right? So take a look at this. That's our asymptote. So we need points. If the graph is here, then it's not here, because it wouldn't be a function. It can't cross the asymptote. So just test the point here. Negative four. Plug it in. So what's f of negative four? f of negative four is six over, I'll do it here, negative four plus three, negative four minus three. So this becomes six over negative one times negative seven, which is six over seven, right? It's very close to one, right? So it's positive. So the graph is, if this is one, is here, right? Well, from here we know the rest. This is an asymptote. That's an asymptote. Asymptotes work like magnets, right? So just imagine this thing being an asymptote here. We'll do it this way. This thing, I'll do it this way. So you see, if this thing is an asymptote, if a function is approaching it, it can't go through it. It can't hit it. It can't touch it. So this is acting like a magnet, so it's pushing it, right? So the function either does this and it's asymptotic to this, gets closer and closer and closer. In general, or does this, gets closer and closer and closer. Sometimes it does, does a head fake or does another head fake this way, right? It can't hit this thing, right? That's what these are. Well, we have an asymptote this way, asymptote this way. So this guy's pushing this way. This guy's pushing this way. This function is here. It's not going to go this way because functions have momentums, right? They're not going to just be here. Sometimes they are, but rational functions are not. They're sort of smooth. Well, this isn't continuous, but it's predictable functions, right? So this thing will just go like this and like this. Gilly boy, are you aching to be banned? Woop, goes like that, right? Cool. Let's do it over here. Let's plug in negative four, right? Oh, sorry. I mean four, not negative four. Four. If you plug in four here, this becomes four. This becomes four, right? That's seven and that's one. So seven and that's one. You get the same answer, right? These things tend to be symmetrical a lot of them, right? So this guy goes here and again, same thing, pushes this way, pushes up. So this thing goes whoop. Cool. Now we need to figure out what's going on here. And the graph, because this graph is here, it's not going to be here. We did it, right? We plugged in x is equal to negative four. It was here. So it's not in this section, right? On the inside, plug in number in. Personally, this is three away. This is three away. So I plug in x is equal to zero, right? If you plug in x is equal to zero, you're going to get what? Plug in it. And this was four, right? Plus or minus four, I guess. f of x is equal to zero. So this guy would be six over zero, zero, three times negative three, negative nine, which is negative one over, sorry, two over three, right? Negative two thirds. No, Martin, for some reason, I see some of the things that come up that are blocked automatically, but you guys don't see them. It's weird, right? Automat does our job for us, which is yeah, right on. So it's negative two over three, negative one, negative two over three is here. Well, that's an asymptote. That's an asymptote. That's an asymptote. This guy's pushing this way. That guy's pushing that way. That guy's pushing this way. This is symmetrical. So this guy's going, okay, I can't go up. I can't go that way. I got to go like this. And you can get other points, check out other points and see what it is. Well, I was mostly being facetious and funny. Can you show me how to find the sum of why my took the case? Maybe you didn't know math. If you didn't know math, Oakland's phone, I'd leave you to, right? Can you do a system of equations? T of cervical, solve for T and W. I think we could, sure. Let me show this other version, too. So we show the whole for a second. Let me do this. Let me erase this. I'm going to kill this. Okay. So just imagine this. Let's assume this was x minus three up here. Yeah, x minus three, m minus three, m minus three. This would have killed this. So our function would have been six over m plus three, right? That's f of x, f of m. So that's our function after we reduced it, right? Now we find the restrictions before we reduce anything, right? Before we reduce anything. So we've already found our restrictions. These two were our restrictions, right? When we get to the end, this restriction is gone. So our asymptote is no longer m is equal to three. There is no asymptote there. There's a hole there because our restriction says m cannot equal three. So when a part of your restriction kills, gets destroyed in the process of simplifying, you have to account for it. And in the bottom here, you would say not an asymptote, but holes. Where do we have holes? We have a hole and x is equal to three. Well, we need to find out what y is when x is equal to three. So you plug it into your reduced function. You get six over three plus three, which is six over six, which is one. So when x is three, y is one is a hole. There's a hole there. Cool? Okay. And then you can go ahead and graph your function, plug in points and see what happens. This thing is going to do, what's it going to do? I'm assuming this thing might go like this. You can find a y-intercept, find a y-intercept. Oh no, there is no y-intercept. Anyway, we could graph this using other points. I just need to make more room. Adios, donor. All right, I have to get going. Okay, Audnick, thanks for popping in. Have a nice evening, guys. Hope you have a fantastic evening, Audnick. These are great. I love these tutorials. Awesome, Lark. Fun. So how did you reduce the function? I introduced this on top, right? I cheated. I just wanted to show another variation of what a hole is, right? What was the other question we had? There's something else here. Oh yeah, this thing. Let's do this. T times W cubed equals A, so T W cubed equals A, and Wt cubed equals B. Wt cubed equals B, and want to solve for T and W? I would just do substitution, right? I'll leave you to it. Too funny. I'm from 9th grade, from Brazil. Hello, hello, Adriaden 93. The whiteboard. Need a bigger whiteboard. Need a bigger whiteboard. I thought it was very important for the future of math. Asymptotes are ridiculously important, right? Asymptotes are important in society, in restrictions, in physics, in restrictions, in chemistry, in biology. Asymptotes and holes are unknowns, right? Asymptotes are important for many things. For example, in stats, the asymptote will let you know how your functions go. Limitations, it gives you limits, right? Is there, for example, for in biology, based on gravity on this planet, there's only a certain size that creatures will grow to be, humans. There's only a certain size that will ever grow to be. You won't find a human on planet earth that's going to, you know, like Giant Man and stuff in comic books. That'll be like, you know, how tall is Giant Man or 80 feet tall, right? Because the bone density in the month, it won't work. If they can maintain the same bone density, it'll collapse, right? So there's a limit to how high, how tall we'll get. Isn't gravity just a theory? No, gravity is a function of matter. Matter has gravity, right? It's just a property of matter, right? It's like time. Time, to me, for me is a property of matter. Space, time, curvature, yeah? So take a look at this. I want to solve for T, I want to solve for W. Let's solve for, here, let's just write this equation in terms of, so number your equation, one, two. Bring equation one down. T is equal to A over W cubed, right? Just divided both sides by W cubed. Chichu, are you telling me Giants don't exist? You're breaking my child's heart? There could be Giants relative to us. There could be 10 feet tall, 15 feet tall. I don't know what that has to do with that boundary is based on the physics that we know, biology of human beings. Like a 15 tall, feet tall person would be a Giant, right? Sometimes I've seen some NBA basketball players. Geez, they're like, they feel like they're really tall, right? So substitute this into equation two. So sub, sub one into two, right? So we're going to kick this guy because that's T, that's T, that's T. Sub that into that. So equation two becomes W times A over W cubed, cubed is equal to B, right? So this becomes W, A cubed over W to the power of nine is equal to B, right? When you're solving for this, don't kill the W's, okay? Just on this planet. Some would disagree. It's mass or buoyancy. It's basing on assumption. Can you prove gravity with an equation? Gravity is one of the hardest things. Gravity is the one that stands outside of the three main forces that we have, right? We've got the strong nuclear, weak nuclear, electromagnetic and gravity. We've been able to, as far as I know, my physics, bring these three together, but gravity stands apart. String theory talks a little bit about this, and according to classical physics, gravity is the weakest force there is, but if you start talking about membrane theory where we can jump from one universe to another universe, then gravity would be the link. So it could be the strongest force there is, right? Gravity is is unique. Gravity is incredibly encompassing, right? Because we are matter, right? So as Goudal says, the inconsistency, you can't look at a system from within a system to find out where the flaws of that system are. We are matter being. We're trying to look at properties of matter from within the system. Difficult to do, right? Mathematics says so. Sorry, I'm back. I'm currently doing some work for the business. Awesome, Spiderman. Do your stuff. Everything's going pretty good right now. I think so anyway. Because you'll lose a solution if you're trying to solve for W, right? So what you do, what you should do is this. Cross multiply this baby up, right? WAQ is equal to W9B, or B, I should write the... Well, I wrote it this way, but A and B are just constants, right? Goudal's incompleteness theorem. I stumble every time I try to say this, right? And then bring this guy over. So we got, I'm going to rearrange this. So we got B, W to the power of 9, negative B, W to the power of 9 plus A cubed W is equal to 0. And then factor out a W. W comes out. Now you got negative B, W to the power of 8 plus A cubed is equal to 0, right? You got two things multiplied to be 0. So one of them is W equals 0. If you killed this W, you would have lost this solution. You don't want to lose a solution. Don't eliminate your variables when it comes to division because you'll lose solutions, possible solutions, right? And then this over here, we got negative B, W to the power of 8 plus A cubed is equal to 0. Solve for W. I'm going to bring it here. So W to the power of 8 is equal to negative A cubed divided by negative B. Then negative kill each other. So W is equal to the 8th root of A cubed over B. Okay. I hope that's okay. I hope I didn't make any mistakes. Spiderman is doing business work. What does this mean? He has his own business, so he's doing work on the side. I'm taking pics for the Daily Bugle. Nice. Awesome. Awesome. Jay Jonah Jamison. He's paying Spiderman not much, but you know, Spiderman's got to do what a Spiderman's got to do, right? Nice, Martin. You were on it too. Do it. Awesome. This is an even power. This is even power plus and minus. Plus and minus. 8th root of A cubed over B. Can it be factored into multiple quadratic roots? I think that really depends on what A and B are. If they're just constants, it's just a number. Two numbers, really. Right? Lemon tea honey. I got to remember when the sun starts shining so we don't schedule any math sessions during the time. We've got a skylight here. So as the year progresses, the light changes. So different times we get sun shining here, so we can't do math. I got to remember when that is. Hopefully, I don't make the mistake of setting a schedule like that. No, not really. But that does explain that most cosmology agree. Cheers. What are you guys snacking on? I mean, can the 8th power be expressed as four quadratics? Can the 8th power be expressed as four quadratics? I'm not sure what you mean. If it was factorable, sure. Me neither. Yeah, I'm not sure what he means. I'm making some tea for the wife. Nice. For the MJ. Well, they were married at some point, I think, Spider-Man. For MJ, chips and yogurt. Super delicious. Tuna and gluten-free crackers. Nice. Then it would just be plus and minus one. Homeless and chips beats that. Homeless and chips is pretty good. But I prefer yogurt and chips. I really like yogurt. So the roots are zero, negative one, positive one. Exactly. That's what it would be. With some of them, repeated multiple times. Yes. And you get repetition here. Not zero, but here. All right. Nice. That's good harvri fras. That's good fras. I hope that's okay if I... Jesus, that's so much sugar. Yeah. Very good. Very good. Very good. Very good. Highly recommended. I don't do this often. We do good math today, by the way. Is there danger in missing out, mentioning repeated roots? Is there a danger? It just... When it comes to the function, what it means is you're bouncing off. You know, it depends on the roots. You're bouncing off. It's off either a point or the x-axis. You're bouncing off the x-axis, basically. Or you're doing a twist through the x-axis. Sometimes it's a bigger twist. Sometimes it's a wider, flatter repetition. It pulls down the function even more, right? And that's the way I look at it. Because I can hear every crunch. Very nice. Do you have a mic? Or is your room just tiny? It's... I do have a mic. It's right here. See this? That's a mic. So we could be picking that up. I don't know if the room's super tiny. It's like an average-sized room, I guess. Let's have a six-pack. 46. Oh, tuna and gluten-free crackers. Yeah. Protein. You get your hardcore protein. Almonds and dark chocolate covered blueberries. Catholic tradition. Yes. If we can solve it, for sure. I don't even know how to pronounce your name backwards. I don't know what that is. X to the power of 9 minus 1 equals 0. I mean, is it just redundant to state it nine times? Yeah, it's redundant. You just say x is equal to 1, right? That's it. I feel boring. I'm just beef and spinach... beef and spinach leaves. Beef and spinach. That's pretty good. What's wrong with that? I might be going crazy, but is there an animal nearby? Not here. I am scrolling with my thing. No, no animals. We did. We passed away a couple of years ago. Our kit. Yeah, kitty cat. Fun stuff. Cattle chips. Absurdacon, you know your chips? Or Miss Vickies. Is this Miss Vickies? I think it's Miss Vickies. Yeah, XQ because one is one. Right? Japanese Italian and Canadian. Japtalian, Canadian. Catholic tradition is deciphered. How do I get the complex roots? I don't believe that one has any complex roots. XQ minus 1 equals 0. Does that have any complex roots? Unfortunately, I'm not dealing with complex roots. In my part of the world, they're not teaching complex numbers. So unfortunately, I'm not too familiar with them. Love kettle chips. Yum. Chips and dip. The best. Yeah. Really is. 2x equals 10. Oh, 10hx. If a is big, find x. Oh, dude. I think that's above me. Maybe Mask of Raven. Audnick would have loved this, by the way, probably. Mask of Raven, if he's still here, he might like this. But that's beyond me right now. Absurdacon is a chip connoisseur. Nice. Chip connoisseur. Salt and vinegar chips are my favorite. I don't buy too much chips because you can gorge on them, right? I do gorge on them. Sour cream and onion. Sour cream and onion. Super good. And salt and vinegar is so good. That deserves a high five. Yeah, seriously. Well done, Catholic traditionist. Rest in peace, chichocat. Yeah. We buried him in the backyard. He's a good cat. Awesome cat. Honorable mention to jalapeno kettle chips. Yo, yeah. Kettle chips are the superior chip. Bro, math is actually fun. 100%. Harvest 376. First, you have one root. x equals one. Then you get x minus one. Oh, you get the Q. Equals zero. So it's the root. But where? How come you got that other function, racer kill? Did I miss a question? Guilty pleasure chips. Original or cheetos? Oh, flaming hot cheetos. Filly free. Yeah, absurdacon. I stopped eating the bad type of chips. Not that these are healthy for you, but the really bad type of chips, I stopped eating them. I'm too old for that chip. I'm too old for that stuff. Have you tried the Korean bulgogi kettle chips? Oh, I haven't tried it. I had yesterday. I no longer have any left today. Oh, I don't know this one. Korean bulgogi kettle chips. What? No, I haven't tried. That sounds fantastic. And bulgogi is a Korean dish, by the way. Super delicious beef dish. Oh, so good. Trig is my only weakness in most people's weakness. You have to remember all trig equalities. You don't have to remember to a certain degree. By the way, real homeless being, if you go to my YouTube playlist, I have a series playlist on trigonometry. Because trig takes a lot of people out, I put out a whole bunch of videos like six hours worth of trig content. I don't know how many hours it's at least four hours up four to six hours, I think, right? Of trig content. Okay. Oh, because you can factor that. That's right. Racer kill. I forgot about that. Thank you. That's right. Those are the complex roots of it. Yeah, we don't... Oh, let me do this. Anyway, the trigonometry, I put out a whole series on trigonometry. I've done the first part of trig. I haven't got into the identity stuff yet and graphing it to a certain degree, hardcore graphing it. But the core of it is there. And once you understand that, the rest of it is easy. I totally forgot about factoring the cubic. Silly chicho. X cubed minus one is, if you factor this, X minus one, I forget what it is, X minus one, and X squared plus X plus one. Plus one. So if you want to solve for this, if this is equal to zero, I'm just going to put it equal to zero here. If you're solving this individually, you would go X cubed is equal to one, then cube root both sides, right? So X is equal to one. So you got this solution, but you're missing this one, the complex roots, right? Well, if this is equal to zero, this is equal to zero, you split them up, right? So you got X minus, oops, X minus one is equal to zero, which the solution is this, and you got X squared plus X plus one is equal to zero. This one, you can't factor manually. So use the quadratic formula, right? If you use the quadratic formula, X is equal to negative B plus or minus squared of V squared minus 4 Acc over 2A which is equal to AB and C. A is one, B is one, C is one, right? So you're going to get negative one plus or minus squared of one squared minus four times one times one over two times one, which is equal to negative one plus or minus squared of one minus four over two which is equal to negative one plus or minus squared of negative three over two, right, which is equal to a negative 1 plus or minus 3i, because i is equal to square root of negative 1, right? Or, sorry, square root of 3i over 2. So your other two solutions are x is equal, I'm just going to write it like this, negative 1 plus square root of negative 3 over 2, and x is equal to 1 minus the square root of negative 3 over 2. So these are the three solutions we get. Sorry about that, I forgot about that, because we're not, I don't, they don't, they don't do this anymore where I am, which really sucks. All right, use it or lose it. Okay, I'm going to scroll down again, wow. Lark, I just, I just know how to do certain things, that's the way I look at it. You realize all the terms cancel and you get solution just dot dot. Oh, there's another one going around. It's supposed to be negative 1 at the second solution as well. Thank you. Thank you liquid swords. Teach your brain part. Me sad here wondering what the heck is going on. Mr. Mersh, how are you doing? Scrolls. In general, solutions to x to the power of n minus 1 lie on the complex unit circle. You can solve such things with trigonometry, for example. Cool, right? Thank you for that right answer. Joe, Nihofat. How are you doing? Can we go back to basics for my smooth brain? Smooth brain, someone's, I heard another student say smooth brain earlier. I didn't realize what smooth brain meant. Basically, he explained it to me, because I don't know if this is true or not, based on biology, the way they figure intelligence and how smart you are is the number of curves you have in your brain, right? Yeah, it's hilarious. I never knew this, right? So my student told me, oh, yeah. So if you have more curves, you're supposed to be more intelligent. So if you have a smooth brain, you're not very intelligent. I mean, you're a researcher. Is that true? Seriously? Real must be. I didn't look at it any further. I like calling it brain farce, right? Do you have a nice problem? Oh, I totally missed out on a nice problem. Oh, man, did I miss something? You did, masquerade. Something came up that I couldn't do. If you were here, you could have done, but I think it was already solved earlier in the chat, but I totally missed it. I was doing something else. I like prime numbers anyhow. That's my bad habit. Prime numbers are awesome. Prime numbers are a core building block of the real number set, right? More curves lead to more surface area, so information flowing, right? But is it all because of surface area? Speed of light pen 1 divided by 0 equals God. If you call the unknown God, the universe exploding God, infinity God, more curves equals more surface area. It's a theory, but it makes sense. Okay, cool. Bot mass. Bad mass. So square root of negative 3 equals the square root of negative 1 times the square root of 3. Yes, that's exactly it. That's exactly it, right? So you have square root of negative 3 is equal to square root of 3 times negative 1. Well, this is equal to square root of 3 times the square root of negative 1. So this is square root of 3 and the square root of negative 1 is defined as I. Prime numbers doesn't really matter for real numbers, because real numbers can be factored arbitrarily. Building blocks for integers is more correct, I'd say. Building blocks for integers. But rational numbers, like what's the definition of rational numbers? They say numbers that repeat or terminate, but really the true definition is numbers that you can write as fractions of integers. So those are governed by prime numbers. So so on and so forth, right? I would still say real numbers. I wouldn't just say integers. And if you're going to take it down to integers, then you just say natural numbers, right? Because integers are negative numbers as well, and prime numbers aren't negative, right? Prime numbers are only positive. So we could say natural numbers. And I do that every now and then. I talk about what prime numbers are the building block of natural numbers and natural numbers are the building block of everything else, right? Speed of light pen is how are you doing? Is this is to find the solution if you have a graph, but you also have to prove your answer? Yes, but keeping in mind that in general, when dealing with the complex, surfaces where all cell bodies exist, okay, allowing for more concentrations within the brain. Ah, so I don't know the biology. My questions would be ridiculous. Is zero natural number? Zero is a whole number. It's a new category they created because it was building on the natural numbers, right? Sure, rational numbers is good too. But real numbers, numbers deals with numbers that aren't rational. Real, yeah, because you have the irrational numbers, right? But the prime numbers are the building block of the irrational numbers as well, right? So for example, what makes a number irrational, right? So if we do this, the root of any prime number that you cannot reduce anymore is irrational, right? So if we got the square root of eight, this is two root two. Well, that's a prime number, right? That's the building block of the irrational numbers as well. Speaking of irrational, can we do proof of square root of two being irrational? Well, it's a prime number. You can't reduce it down anymore. So it's irrational. I'm not sure, I'm not very good at proofs. I just, if it's a root and you can't reduce it anymore, it's irrational and you can't reduce it because it's either a prime number or prime numbers multiplied together, right? But you can't reduce it anymore. Rational is able to be noted on paper. Are there trolls coming in? It's magic. It's wild to me that it's a real number. It's irrational. No, that's a fraction of integers, so it's not irrational. No, if you have integers, five, six, just because it doesn't divide evenly, it doesn't mean it's not, that's integer. Integer equals rational. If it can be written as a over b, it's rational. Yeah. Sorry, Martin. I've been lurking, doing stuff. What's going on? Yeah, I don't know. I haven't seen too much troll action. I think Martin might be zapping right away. Zero is a number, but it is not an amount, correct? How much money do you have in your pocket right now? Zero dollars? So zero amounts? Guys, the natural number sometimes includes zero. Sometimes not depends on what your definition depends on, I guess, which part of the world, which system you're learning this from. It's astounding when you think about prediction. What's the topic tonight? We did a lot of math, Slayer. I would like to order zero of those, so here you have zero dollars. Yeah, that's astounding. If Martin is getting overwhelmed by trolls at any point, just give the Chichonian battle guy and it won't come running. I have stream volume one. Nice. What about negative numbers? Negative numbers are integers, or they could be integers, I guess. So what time is it? The sun's coming in. So 3.30. So no setting up math streams starting at like after 2.30. I've got to remember that. Oops, I could give you a couple of proofs in Discord if you like. Lots of discussion going on. Lots of discussion. Fun stuff. Should we call the stream gang? Let's call the stream. I think we did lots of mathematics. A lot of discussion. Fun stuff. Thank you for being here, gang, by the way. It was great. Very much enjoyed. Thank you for the subs. Thank you for the follows, gang. We're going to be here tomorrow as well from 1-3 doing math. Okay, so if you want to do more mathematics, if you know someone that's having a hard time with their high school math or they need help right now, they're in lockdown mode. They're trying to learn something that they don't have the people that can bounce off ideas from. There's people here that are willing to help. There's some people here that know their mathematics stronger than I do and they're giving their time to help people out. So feel free to pop by. I think we're all in the mindset of everybody speaks the language of mathematics. If everybody in the world was littering the language of mathematics, the world would be a much more beautiful place, so we're working towards that. Aside from that, wonderful. Look forward to your awesome, awesome. Aside from that, active on Patreon, that's where you can follow the work. If you have the funds to support this project through Patreon, fantastic. Very much appreciated. If you don't, you can just still follow. I don't put anything behind the paywall. I believe in free sharing of information. So you can just follow the work and whenever I post stuff, you'll get a little notification that we posted a video or talking about something or whatnot. Slowly I'm going to be building up the curriculum on Patreon. We are live streaming on Twitch. If you're watching this thing on another platform, it may be YouTube, BitShoot, or somewhere else. So if you want to interact with everybody live during the chat and participate in these discussions, Twitch is where you want to be at. I do announce stuff on Twitter, Gabs, Minds, VK, and Elo. That's where the announcement platforms are in, where I'm sort of shouting out and letting people know what's going on. You're very welcome, everyone. Thank you for being here, by the way. And I'm uploading these things on YouTube and BitShoot right now. Whatever BitShoot is able to process, sometimes there's hiccups. And whatever I feel safe right now to load on YouTube without being deep platform, we'll see where that goes. Hopefully the sensors don't zap us. But if they do, come to BitShoot. It will be there. It'll be very unfortunate, but hopefully it doesn't happen. And we will introduce a third one at some point. Do we have a Discord command? I think we do. We should. Let's try it out. Discord. Nice. We got a Discord command. And right now, there are certain healthcare systems in the world that are being overwhelmed. If you live in those areas, keep a little bit of physical distance, just so you don't overwhelm your healthcare systems. If you're lucky enough to live in an area where there isn't too much happening, be aware that things could be happening. And there's something going around. If we don't know exactly what it is, be cautious. And make sure you're paying respect to all those people that need to be out there taking care of business during a storm that's going through the world right now. Be kind, everyone. Aside from that, mods, thank you very much. We wouldn't have this platform and this discussion going on without the mods. So huge props to the mods, man. Very much appreciated. Scrolling command. Okay, I'll try to remember. So we'll talk on Discord. Let me know what it is we need more. And then I'll go into Nightbot and set something up. Scroll, meaning scroll all the way down to the bottom? Or automatic scroll? I don't know. Talk on a Discord? Okay. Be kind. Please rewind. Be kind. Please rewind. Those functions are not quadratic, right? I don't know. Yes, especially be kind to others during these troubled times. 100% luck. 100%. Aside from that, gang, I'll see you guys tomorrow if you can make it. Otherwise, we've got four streams in the next four days and the times are on Discord and counting down on Twitch and definitely on our Patreon page. Okay. Bye, everyone.