 and we should be coming out. Hi everyone, this is Chichop. Welcome to my channel and welcome to another live stream. Today, today is March 22nd, 2021. And we're doing our math drop-in tutoring session number 72. Let's do a little mathematics. Let's see what this is all about. And as the numbering goes, we're around the number 72 of these that we've done, which is basically me making myself available for a couple of hours, around twice a month, sometimes three times a month, to help people out if they need a little bit of help with high school mathematics specifically. But we do touch into a little bit of calculus, a little bit of statistics, as well as some additional stuff in higher level mathematics. And of course, elementary school mathematics is also a game, which is basically, you know, understanding the basics of algebra and dealing with fractions, primary factorization. It should be a lot more elementary school. They should teach a lot more mathematics, a lot, a lot more. But they're not right now in my part of the world, which is Canada in the United States. As far as I'm concerned, coming out of grade seven in the elementary school, that's when the kick out is into high school. Coming out of grade seven, you should know approximately almost all of the most, the important chunks of grade 10 mathematics. So you should already know, as far as I'm concerned, in grade coming out of grade seven, how to graph a line, how to factor polynomials, what polynomials are, what functions are. That's what it should be. Unfortunately, people coming out of grade seven in my part of the world barely know how to solve for x for just one variable equation. Something we have to remedy, which is what these math sessions are about in large part. Aside from that, welcome to another live stream. As far as who I am, what this is about, I am on Patreon. Patreon.com forward slash chico, c-h-y-c-h-o. If you want to support this work, if you want to follow this work, if you want to know what this work is about, which is layer on mathematics. Patreon is a great way to do so. I don't put anything down, paywall, everything's great in common, share and share alike. And for those of you that want to support this work on Patreon and gang, thank you for the support. It is in large part because of your support that we're able to do this. We'll see where it takes us so far, so good. And we are slowly rolling out a lot of related content. Maybe through comic books, maybe through some of the math videos we're doing. We just spent two and a half hours, a couple of days ago, or yesterday, putting together a summary, sort of a exam for one of the modules that we're going to put together. Fun stuff, fun stuff. And we are live streaming on Twitch. If you want to participate in these live streams, as they are happening, Twitch is where you want to be at, twitch.tv forward slash chico live, c-h-y-c-h-o-l-i-v-e. For those of you that want to support this work on Twitch, gang, thank you very much for the support, for the follows, for the likes, for subscribing, for coming to these live streams and mods, for taking care of business. I do announce these live streams 30 minutes before we go live on Parler, VK, Minds, and Gap. You can follow the work there and we do have a Discord page. So sure, we do have a Discord page. You can go to our chat anytime you want and type in exclamation mark social, and all those links will pop up, including the Discord link there. You're welcome to join us. If you would like slick mech chico, thank you for your kind words on Discord. Health mental channel last night. Ah, my pleasure, slick mech. Making the decision to drop out and return in a year after working to steady math in a more relaxed, practical university, lots of love, man. Can't wait to see this one. Awesome, slick mech. Make sure you fulfill on your promises if you think that is really what you want to do. Make sure you don't get caught up in the lazy sort of mindset because we do as human beings, we do have a sort of a lazy tendency, right? Like for you, just to let you know, for me, and just to fill people in. It's okay. I'm assuming it's okay, slick mech, if I fill people in really briefly. Is that cool? Because you posted on our Discord, not open, so I'm assuming it's all good. But I'll wait until you tell me so before I proceed. Okay. Just finishing off our little intro. We do upload audios of these live streams if we don't have any visuals, which we do today. When we don't have any visuals, we do upload the audios to soundcloud.com forward slash chico, ch-y-c-h-o, as podcasts and those podcasts should be available on your favorite podcasting platform, including Spotify and iTunes. Slick mech chico, of course. Share and share, like awesome slick mech. Just to fill people in, slick mech yesterday, sort of yesterday, day before, was on our Discord under mental health. I guess it was. I'm not sure if it was under mental health or education or mathematics, sort of asked a question. His heart was not in being in college right now, right? He was struggling with it for obviously reasons, right? There's so much going on in the world, right? And just centralized education is not rolling out nicely into sort of this new paradigm shift that's being rolled out, right? So he mentioned that he's having a hard time trying to come to grasp with wanting to drop out and wanted to convey how he feels to family and friends for them to understand why he's feeling this way that he needs to take a break, right? And I just sort of posted a little thing saying that it's okay, it's okay to step out, right? Take a break for a little while, but if you do want to, you know, it is something that you want to be into, make sure you go back into it, right? So just to expand on that, just to let you know where I was when I went to post-secondary education, right? I graduated high school and I got accepted into university right off the bat, and I've shared this before, but I'll share it again because the topic is there. I went to a university right away, right? And when I went to university, it wasn't like the university I went to was very high school-like and I was really tired of high school. I was done with the whole bubble mentality and the childish. I was sort of done with it, right? But this university was very high school-ish, right? And I didn't find it to be motivating me at all. Slickmick, thank you for the tier once up. I appreciate your support, brother. So I didn't find there was any motivation for me to continue my studies at university when I went there, right? Yonar, thank you for the follow. Except for two courses, geology and geophysics I was into, right? Physics, mathematics, chemistry, English. I just couldn't get the motivation to do anything in these things, right? And I was getting stressed out. Like I really didn't like it. It was stressing me out, right? And this was a younger chichou, right? So I was a little bit more fiery, right? So I was getting a little stressed out and just not happy about it, right? There's times where I would drive all the way to university days and it's like a 45-minute drive and I really enjoyed the drive. It was like windy, 45, sometimes an hour, get there and I parked the car in the parking lot and I go, ah, the hell with it. Turn on the car again. Back home. I go to do whatever I was doing, right? Or go meet up with friends and whatnot. So after doing this for a year, right? I decided to drop out of university, but I didn't just drop out and, you know, pick my nose, right? I dropped out and this wasn't sciences. So I decided to, you know, go to college, right? University and college is different here. You go, college is, you know, it is sort of classified as a lower level than university, but to me it's not. It depends on what you do with your education, right? How you're studying. But anyway, the category is usually you go from college to university. I went from university to college and people were freaking out. And I went, instead of going staying in sciences because that's something I was in all the time, I went to, I enrolled in a business program, right? And after two months, I realized I didn't want to be in the business program. This was silly, right? So after being four months at the college, I just dropped out and people freaked out again. I couldn't explain to people why I was dropping out, right? You explained it to them. They're like, oh, you're crazy. You've got to end up, especially family. Family was like, oh, what's this guy doing? And, you know, the poop hit the fan when I wouldn't got a job as a graveyard shift in a gas station across a reservation, native, indigenous, native. I don't know what the correct terms is anyway. We call the, we call the reservation at the time, right? Across from a reservation, which was a lot of conflict, right? There was, so I witnessed for six months I was there, I think. And graveyard shift from 11 p.m. till 7 a.m., lots of interesting things happened. So someone, you know, basically fresh out of high school, it was a pretty cool place to be and I read books. I read Lord of Rings, right? I wanted to read all three books. I was a really slow reader. So I was building on myself, right? People didn't, couldn't understand this. I told people, oh, I'm there. It's really interesting, you know, seeing what's going on, right? Crazy cool, right? I saw accidents. I saw this. I saw that. It was crazy, right? And I was reading books. But you couldn't explain that to people that, look, I need to take time off to read three Lord of Rings books. I'm a slow reader. Coming out of high school, they didn't really teach me how to read properly. So I have to teach myself. So I'm learning, right? Nobody understood, right? After that, I took some time off, went on a little vacation, saved some money, went on a little vacation, and then I enrolled back in. I got my geophysics degree with a minor in mathematics. That was my path. Okay, just to expand on that, I wasn't going to type all that out. That's where I came from. And I don't think that's the path that everyone should take. But that is a path that is there, right? Which is a path that a lot of people do not talk about. Verdi here recently, read a great saying, goes something like, quote, everyone is in a rush to climb to the top of the ladder. Not many stop and check is the right ladder for them. Imagine spending your life to get to the top of the ladder to realize it's the wrong one. End quote. 100% agree, Verdi here, right? When you come out of high school or university or college, everybody needs to take about two years off to think about who they are. Realize how you want to interact with the world. You've been in a prison system to a degree, indoctrination, regimen. You actually acquire your freedom when you come out of high school for the first time ever. Some people go directly into college university. Some people go to apprenticeships. Some people go to work. Some people go travel, whatever it is. But it is your choice now to do that, right? Think wisely and realize that the first choice might not always be the right choice, right? Slick Mac. In Ireland, we go high school, straight to a college or university. I think that a year might help me to develop personal and mature, especially to read. Sorry if I sidetracked you, ready for some math whenever thanks for the great words, Verdi too. And this is not sidetracked, this is education. And as far as I'm concerned, it's all education, right? Believe it or not, when I get hired to teach people mathematics, mathematics is maybe 30% of what I'm really sharing. If the student listens, 70% is about life. And people who have problems in high school and stuff like this, it's not really content related. It's system related, right? It's a structural issue. So this is structural discussion. Fire exit. Did you learn to read later in life? Or is reading something that didn't click for you? By the way, I'm a slow reader too. Fire exit. When I came to Canada, I was in grade five, 10 years old, almost 11, right? I didn't know how to read and write English. I knew how to read and write Farsi and speak Armenian and Farsi. And when I came here and, you know, grade halfway through grade five, six, seven, and I get into grade eight and then they say, I have to learn French at the same time, right? Oh, you have to take French as well. I'm like, man, I'm just starting to learn how to do English. And they're like, no, you have to do a second language. I go, well, I already have two other second languages. You know, pick one. Armenian or Farsi, you know, like, I'm willing, you know, I know those base. I'll learn those better. They said, no, we don't recognize those languages. Just imagine a system centralized system coming up to Chico in grade eight and saying, we don't recognize your language. My response was, well, I don't recognize your ethnic language either, right? It was more confrontational for me. I took it as what a, I woke to the limitations of the system early in life. And again, we will be uploading this video to SensorTube, Pichu, and Rumble. And at some point to Odyssey as well. And you can support this work on those platforms by liking, sharing, commenting, subscribing. And if you're on SensorTube, you can join SensorTube membership and there's a button there. And just a heads up regarding SensorTube. It's having hiccups. We're slowly being demonetized. Okay. The algorithms, the automation is going through some of our videos and picking up some things. And there's a lot of, in school used to call them rats, things, people who bow down to centralized authority. And they rat people out, right? Just because they don't agree with, and usually those people who are ratting people out, they're not bootlickers. They're not, they really don't have a perspective on life themselves. They are just minions of the centralized authority, right? So I guess some of our videos are being flagged. One of them was giving advice on how to deal with a bully. People were freaking out about that, right? So that was demonetized after that. And before that as well, we've been getting zapped a little bit. So right now, SensorTube algorithms is going through our videos and it's having glitches, right? So slowly what's going to happen is I'm going to reduce the amount of content even more so loading on SensorTube. Just a heads up, the odds are politics is not there anymore. The odds are personal finance and economics will not be there anymore. The odds are some of the life discussions we have will not be there anymore as well, right? I'll see how the glitches go with this. And they're rolling in this tax thing that you have to fill in the Google's tax form. You know, telling about your tax situation for them not to take off American taxes in Canada from your... And I'm not going to go through that. Tax information is personal. I have no desire to share that with Silicon Valley. I haven't gone through the click, so I don't know exactly what they're asking. Maybe it's not that personal, but I'll deal with it as it happens, okay? Just a heads up for the gangs on SensorTube. You're watching this on SensorTube. I highly, highly recommend stop watching it there and watch this content on Bichute or Rumble. There are no advertisements on Bichute, and I believe ads are kicked in for Rumble, right? And one other thing, if these glitches persist on SensorTube, I will... I know, I didn't do it YouTube. SensorTube was doing it automatically without my hearsay going into previous videos and monetizing in-roll ads. I only, for 15 years when they're... I don't know how long ads has been available on SensorTube, but I've only allowed ads to be run on my videos at the beginning of the videos, right? If these glitches persist on SensorTube, then what that means is they want to maximize their revenue intake while limiting your freedom of speech. So we're going to start reducing the amount of videos we're going to load on SensorTube, right? So we're going to reduce the type of videos we're going to load on SensorTube, but action, what is it? Action, reaction, solution? Solution? We're going to stop reducing the number of videos we load on SensorTube, right? At the same time, to get those SensorTube algorithms kicking in so they will actually promote our videos, I will most likely go back and place in-roll ads on all of my videos, right? And whenever I do that, for any video I do that, I will provide an option for people to watch those videos on Bichuto Rumble, ad free, right? So be warned, I'm about to roll in some changes on SensorTube as a reaction to what centralized authority power is doing, right? It is what it is. Heads up. Really interesting, thanks for sharing my pleasure fire exit. Aside from that, that's our little update, I guess, right? That's a update of what's going on behind the scenes and history little updates regarding education, right? Let me take these guys down. And we're here to do mathematics. If you want to talk about mathematics, if you want to talk about anything else, anything else is game, it is an open discussion. Just know that mathematics supersedes anything else. So if someone rolls in when no matter what we're talking about, someone rolls in with a math question, we can deal with a math question. And if the topic of discussion is too sensitive to be loaded on SensorTube, so be it. We'll not go on SensorTube. And I might start loading on some videos on TikTok. I just got to get the app loaded. Unfortunately, I have to do some things on my phone to get the app loaded because I can't figure out how to do it on a desktop. It won't let me emulate it to change the profile and do this. So I have to go through it on a phone, pooper-scooper. And a couple of days ago again, here, let me show you what we did. This is math related just to give you a heads up because there's no math questions right now. Now, one of the things when planning to do with all the math content, this is something that's been in the works since day one, me loading this up, was basically we're going to create modules for mathematics, to teach mathematics, right? So a few days ago, last week, basically, I went on one of my long walks and laid out one of the sort of a summative, sort of a final test or a summary practice test that we would sort of the layout for that I'm going to put together regarding factoring specifically, right? What the concept of factoring is and we've created a lot of videos for this, started back in 2007 with series one of the language of mathematics and we continued and series one of the language of mathematics, the first part from 2007, 2008, and series three A and three B, as well as two as well, have a lot of stuff related to factoring in polynomials, right? Slick Mac, it's amazing how so many great 12 level people I know can do math and have no idea what they're actually getting. Why should be a fundamental chapter in all math books indeed? What does solving for X mean and why am I doing this? What are the practical applications of this formula and why am I being taught this? My two cents, Slick Mac, I 100% agree. That's why when I started creating this content, I broke up the content that I was creating into two different categories, the language of mathematics, which is the syntax of the language of math, right? How it works, right? Algebra, if you want to think about it. And the other one was math in real life, which is taking the syntax of the language of mathematics and applying in the real world, right? So we've created some questions before on that, right? And we've created a lot of content on that. 20 CO2 redeemed, 1000 points. Thank you for redeeming the points. And for those of you who are accumulating points and redeeming points, just keep in mind that at some point this year, just like last year, we're going to do an auction, sort of a viewer appreciation and auction off items. And you can redeem them, win them, or bid on them using your point system. So you can save your points or redeem them up to you. Just to let you know. But what I ended up doing for the summative, sort of a summary test wanted to do. I sort of went on my long walk and I knew I already know how I'm going to create all this because I've been doing it for 20 years teaching my students, right? So I laid down what I was going to do, right? Sort of point form. And a couple of days ago, we went through and we put that exam somewhat up together, right? So this information here is 15 pages, right? We sort of made this, created this live, okay, while we're live streaming on Twitch. I'm going to have the video up on SensorTube, Pichu, and Rumble. So basically it's a two part summary, right? You would have my crazy chicken writing, but the language of mathematics would be part one and math and real life would be part two. So the language of mathematics goes through, you know, the different sections, right? Section one is going to be prime factorization, factor the following, and then applying that principle of prime factorization to reducing fractions, simplifying radicals, right? We put some questions together and we did the answers as we went, right? And then the next part would be factoring polynomials, right? And polynomial factoring is basically six different methods of doing it, right? One or A would be greatest common factor and then difference of squares, okay? And that's the way I would teach this chapter, right? And that's the way I do teach this content. And then simple trinomial factoring, complex trinomial factor, right? Can we talk a little bit about complex numbers? We can a little bit. Are you comfortable enough to talk about it or would you need to brush up on the practice? I would need to brush up on it. Slick Mac, very unfortunate because I knew the content really well 20 years ago when I was teaching it, right? Unfortunately, they took it out of the curriculum. They took it out of curriculum about 18 years ago, 19 years ago, right? So I studied it. I've used it in electromagnetic, magnetic methods and stuff like that. Really, as a geophysicist, I specialized in magnetic and electromagnetic methods, right? And I used it a lot. But I stopped doing geophysicists about 21 years ago and I got into teaching math. And for one year, it was still part of the curriculum when I was teaching it, and then they took it out. They've done down the curriculum in my part of the world again. They're teaching about 30% less content in every chapter, every grade, okay? Probably every chapter, every grade in high school in Canada, Western Canada anyway, British Columbia, okay? They eliminated huge chunk of the curriculum that still was being taught 21 years ago, okay? And over time, they've pulled stuff out, right? In the same time frame, right? And people wonder why we have such problems. Maybe just the imaginary number I and what it represents. Yeah, we could talk about the imaginary number I. No worries. I'll save it for another stream. I got to catch up on those things, right? And then here, we'll talk about that. And then the next one is using quadratic formula here. I'll run you through this. I'll have this stuff up. The pics of these up on our discord page, most likely. And at some point, I'll formalize these instead of being handwritten. It'll be like text, or maybe someone can do it. I have no idea. Then we've got synthetic division, right? So this is everything we created. We did two streams ago, right? Two days ago, or yesterday, yesterday. No, yesterday we had a break. Two days ago. Yesterday? No, yesterday we did minerals. Two days ago. We looked at minerals on their magnifying lens, right? And then we have solving for X, which is just simple algebra, right? And then solving for the following quadrics. So you go from simple algebra to a quadratic, some extra power of one, right? And then more polynomial, higher degree, solving for higher degrees. And then we went into graphing polynomials, right? So graphing a line is this one. Graphing quadratics is this one, the way we're going to present it, right? Which is really important. Quadratics is lines linear and quadratics, right? And then we have graphing a higher degree polynomials, right? And this part uses synthetic division that we did already. And then you get into part two, which is math in real life, right? What you're going to use, all of that will be the syntax of the language of mathematics. How do you do this stuff? And how do you go about it, the technique, right? And then taking that technique and apply in real world. First place we apply it with quadratics is maximizing area, right? Maximize an area given a certain amount of fencing. And there's two methods of doing this, right? Method one is completing the square. Method two is finding the X intercepts. And then the other ones that we ran out of time after two and a half hours doing this hardcore, you know, there's these ones. I've already done maximizing revenue, projectiles. You can do consecutive numbers and do all kinds of stuff like that, right? So it's fun laying it all down. It really is. And it was pretty, pretty cool going through it. And gang, don't forget. And sensor tubes, algorithms might not like this, but don't forget, don't forget. Free Assange, Free Assange, Free Assange. Julian Assange is a publisher and journalist that is being crucified for trying to bring transparency and accountability of capitalist power to humanity. For more information, see wikileaks.org, defend.wikileaks.org or our Julian Assange and WikiLeaks playlist on censor tool as for imaginary numbers, complex numbers. Take a look at this. What's the square root of four, right? Hopefully you can see this well enough. These pens are a little bit sharper, right? How do you take the square root of four? Well, when you want to take the square root of anything, it's called prime factorization, what we talked about in the first part here, right, a couple of days ago, you break this thing into things multiplied together to give it the top number, right? And square root means find two things that are identical to give you the multiply each other, right? Select mech two, right? So square root means a pair inside the square root symbol can come out as a single, right? So this comes out as a two. So the answer to this is two. Now you have to think a little bit and decide if that's the only answer you have, right? Because what you're trying to do here with this number is break it down into numbers multiplied to give you that number, right? So here's another option for the square root of four. Do you think of two other numbers that multiply together to give you four that are identical? So two other identical numbers that multiply together to give you four. We have two times two gives us four, right? What are two other numbers that multiply together to give you four? Put equally right as four to the power of a half, I think? Yeah, indeed. Because the radical as we talked about, right? That's a power. A radical is this number just goes in the denominator and the power, right? So if we write down three to the power of two over, I don't know, let's go three. Instead of going three, let's go 90. What do we want? We want a number that's actually, let's go 30. 30 to the power of two over three. You could rewrite that as cube root of 30 squared. Okay, that's what it really means. Chichu, I need to chill here for a bit. I just sent you an emotionally charged rap via DM. I kind of got out of control with my energy. You need to calm down. Time to learn some math. Time to learn some math, maybe, mother. And depending on how big of a rap that is, I might skim through it. I might read the whole thing. Right? What's square root two by square root two? Give root four or would that give root two? Would say that again. Would square root two, I recorded it, just one verse. Ah, one verse. Okay, also. So Snick Mc says, would square root two by square root two give root four? Or would it, would that give two? It would be both, right? So square root of two times the square root of two is equal to the square root of four, which is equal to, now it's not just two. Square root of four is not just two. Because as I asked, what are two other identical numbers that multiply together to give you four? Well, negative two times negative two. Okay. Negative two times negative two is four. So you could write this as negative two, negative two times negative two. Well, two identical things, that's what the root symbol means. This many identical things can come out as a single thing. Right? So this would be negative two. So square root of four is really positive two and negative two. There are two answers to this. Right? Should we do a quick review of radicals, roots? Let's do a quick little review of roots. Okay, before we go, before we go any further, how's this stuff? I'm using new markers. I'm not sure if I really like these markers. They're hard to come off. We might revert back to the other markers. Let's check it out. Oh, yeah, these are really hard to come out. Okay. This isn't, this isn't dry erase. This is a difficult dry erase. Chisho, you should look into the proof of numerology with regard to three, six, nice. Yeah, I've seen it in the past before, brother. For instance, that, yeah, yeah, I've seen it before in the past. It's cool stuff. There's a lot of patterns and I rarely use any of these. I don't think there's anything left in this one. I think I got a little one here. Do I? Let's check it out. Do we have a little one here? Oh, we'll do that a little bit here. It's rare. I use these. I only got these things because sometimes you buy these things in packs and they come with it, right? And it's cheaper buying it with this stuff than buying those things solo, right? The markers solo. Oh, look at this nastiness. Let's bring out a napkin. We're going to do this with a napkin. The name of the wrap has elevated your brain and you're thinking 45 sets of me. Let's talk about radicals. Let's talk about radicals. Yeah, definitely don't like these pens. Also four plus five is nine. Fun, fun. Let's see what we got. Let's see what we got. Let's see which color is going to come out better. Let's talk about roots. Now think of radicals as this, right? Radicals are basically any number in the denominator and the exponent is a radical, right? So if I write down 27 to the power of one over three, okay, then think of this as this three goes in the radical. So this is really the cube root of 27. Well, what's the cube root of 27? Cube root of 27, you break down 27, right? And thank you for the follows game. Apologies if I'm not catching. Those pens are poop. They are. I need a new batch. I got to go get another batch. So break down 27 again. The things multiplied together to give you 27, right? So 27 becomes three times nine, three times three, right? So 27 is really three times three times three. Now this number for the radical up here, if there is no number, it means square root. It means two, right? So when there is no number, it means two. When they put a number, it means whatever the number is. And what that number means is if you find this many, this many of the same number inside, it can come back as one thing, right? So this thing says three things can come out as one thing. So three threes come out as a three, right? And there's nothing left in there. So the answer is three. So the cube root of 27 or 27 to the power of one third is three. Let's do a more complicated one. Let's go 32 to the power of two over five, right? Well 32 to the power of two over five says this. Take the fifth root of 32 and then square it. That's what it means. And usually you do the denominator first. You take the radical first because it makes the number smaller. So the smaller the number, the easier you can deal with it, right? So fifth root of 32. Well 32 is four times eight. Four is two times two. Eight is two times two times two. Well if you're looking for five of a kind, because that's what the fifth root says, if you're looking for five of a kind, here's five twos. Five twos merge into one two. Five of a kind becomes one. So this is two squared, which is equal to four. Okay. Let's do one where it doesn't work out to an integer, right? What if you had... Let's do this. Let's go 32 to the power of one third, right? So again 32, but this time we're looking for three of a kind. So this goes in here becomes the cube root of 32 and 32 we already know is five twos, right? One, two, three, four, five. Two, two, two, two, two. There's five twos. Well cube root means three of a kind. Three of a kind can come out as one thing. So three twos come out as a single two, right? And then what do you have left on the inside? You got two times two. Can you bring those out? No. The cube root says they need to be three of a kind for them to be able to come out as a single thing. So whatever that can't come out is still in there. So two times two is four. So this 32 to the power of one third is two and the cube root of four. Does that make sense? I hope so. That's basically radicals, right? Now let's look at how the imaginary number comes into play here. Easier to take off, much easier to remove. Now take a look at this. So what if we had what if we had as before square root of four square root of four or four to the power of one half. Let's lay it all out from beginning, right? Just link everything up. So what if you have four to the power of a half? This means the square root of four because the two comes in the radical. But if it's a two, you don't need to write it. By definition, the square root just means two, right? So two numbers I multiply to give you four are two times two or negative two times negative two, right? Two times two is four. Negative two times negative two is four. So we have two possible answer plus or minus two. Okay. Now what if you had this? Negative four to the power of a half. Okay. So the whole thing to the power of a half. Keep this in mind that negative four to the power of a half, because this negative sign is not being taken to a power of a half, the way you write this is negative square root of four, which is going to be negative plus and minus two, which is really going to be minus plus two, which is the same thing in plus and minus two. It doesn't make a difference. So the negative sign in front here really doesn't change the game at all, because plus and minus two is the same thing as negative minus two. So you never really write down negative minus two. So you write down plus and minus two. Okay. What about this guy? This guy says this. What's the square root of negative four? What's the square root of negative four? So what are two numbers I multiply to give you negative four? You can have two times negative two. My mood on a scale of 10 is always five, plus and minus five. Hopefully you hit that range in between a little bit too. So it means you're either zero to 10. No, no, plus or minus five would be you hit everything in the middle. So zero to 10, which is great. You're not only, you're part of the, I guess integers would work as well, but the real numbers set and everything in between. So two numbers that give you negative four are going to be two times negative two, but that doesn't help us up because the square root says if two things are the same, you can bring them out. That doesn't work. Or negative two times two. Which is the same thing as two times negative two. So that doesn't work out. We can't bring it out. So instead of two numbers multiplying to give you four or negative four, what do we look at three numbers that multiply to give you negative four? What are three numbers that could multiply to give you negative four? Well, you could have two times negative two times negative one. Well, that gives you positive. That still doesn't work. We need it to be negative. So how about negative? So you can have negative two times negative two is positive four times negative one is negative four. Cool. Well, square root function is just defined to be the positive square root, mainly because it's nicer and lets it be a function. It's only system, system veil. They only say positive up to a certain grade. After a certain grade, you have to look at it as plus and minus. You have to look at both options. I wish they taught that earlier. They always say us. We define it as being the positive, but it's only a positive in certain systems where the negative is not allowed. In other systems, if the negative is allowed, it could be negative. So what I tell my students is I start teaching them this in grade nine and grade 10 because in grade 11, you have to look at the positive and negative. Why do you have to look at the positive and negative here? Let me write this down. What a beautiful equation this is for formula. x is equal to negative b plus and minus the square root of b squared minus 4ac over 2a. Can you appreciate why it has to be positive and negative now? Because when you're solving and this is the quadratic formula, the quadratic formula allows you to solve for x when given a quadratic equation. The plus and minus comes into play because if you have a quadratic formula, which is really a parabola, something like this, this x value is really giving you the x intercepts. It's giving you this point and this point. The way you get both those points is because you have plus and minus in this quadratic formula and the plus and minus plays like this. This is the axis of symmetry for a quadratic equation. Negative b over 2a is your axis of symmetry and plus square root of b squared minus 4ac over 2a is this distance here and minus is this distance here. It gives you both directions. Important. The plus and minus. Where are we? The plus and minus is important. They just don't tell people how important it is until later on, which is unfortunate. They should be teaching this in grade 8 and 9 and people should know it well in grade 10. The plus and minus appears in the quadratic formula because you took a square root, for sure. If you didn't take a square root to be only positive, the quadratic formula would be wrong. But by definition, if you take the square root, you need the plus and minus. The plus and minus doesn't just come into play in the quadratic formula. It's part of what happens. It's the reality of the situation. When you take the even root of any number, you're always going to get a plus and minus. It's there. You can negate the minus. You can eliminate the minus if you want. Really, you can eliminate it or dismiss it or say it doesn't apply in your system. But you have to appreciate that it's there and by applying the language of mathematics, because this is just straight-up syntax. That's what it means. But by applying the mathematics in the real world, you can decide to accept the negative or not accept the negative. Let me try to reword this. Reward it. Yeah, yeah, yeah, yeah. That'd be cool. System veil. Plus and minus appears. Let me read what you wrote before as well. Again, the plus and minus appears in the quadratic formula because you took a square root. If you didn't take square root to be only positive, the quadratic formula would be wrong. If you didn't take the square root, the square, if you didn't take the square root, that's the square root. If you didn't take square root to be only positive, yeah, if you only took the square root to be positive, then the quadratic formula would be wrong because you wouldn't get this other half of the quadratic function. You would only get that half. Let's see what the rewording is before we move on. I like math tensions. They're cool. Let me finish this off, and then we'll deal with that while the rewording comes in. Now take a look at this thing. Here's three numbers that multiply to give you negative four. Here's three more numbers that can multiply to give you negative four. Instead of having a negative two here, get rid of the negative two and go times negative one. So negative two times negative two is four times negative one is negative four. So this works out. Two times two is four times negative one is negative four. So this works out as well. While the square root symbol says, hey, if you have two things that are identical, you can bring them out as a single. So here's two negative twos. They can come out as a negative two. Here's two positive twos. They can come out as a two. So again, we have plus and minus two. Plus and minus two. However, in both situations, we have a negative one still in the square root symbol. So square root of negative one. Now there aren't two numbers that multiply to give you a negative number. Negative times a negative is positive. So this is a special number that appears. And our definition, it is a definition that we've come up with. We say, you know what, let's simplify this instead of because this appears in a lot of places. It comes up a lot, right? Square root of negative one. Electro-dynamics. Electro-dynamics. Electromagnetics. Magnetic methods of water, electricity. You get the square root of negative one in play in the real world. Okay, when you do the mathematics, and when you do quadratics, you get the imaginary numbers coming up and stuff, right? So what we did, because this appears a lot, just like the number pi, right? This is pi. Everyone knows what this is. This is 3.1415 dot, dot, dot, right? We don't have to write it down by decimal places. We just come up with a symbol to represent pi. Well, we just come up with a symbol to represent the square root of negative one. We call it i. So by definition, i is equal to square root of negative one. So to simplify what we wrote, we can write it as plus and minus i, right? Plus and minus, plus and minus 2i, right? So all we do, we just replace the square root of negative one by i, okay? And in mathematics, whenever you see i with a number or just i by itself, we define it to be the square root of negative one, okay? That's all. And then there's different ways you can look at this. You can look at it as the third dimensional plane that's graphing in and whatnot. Unfortunately, I used to know how to apply this. We did apply it. We graphed it and stuff like this. And it definitely comes into play in electromagnetics and stuff, because we graph. We actually provide graphs of the complex number readings that we're taking, because they provide a certain type of information, give us more information about anomalies that we're looking at. But I haven't been teaching it for like 20 years now. They took it out of the curriculum, so I'm, you know, and I haven't done geophysics for like 20 years. So I'm not going to apply this, okay? I hope that's clear regarding i. That's all i is. i is the square root of negative one. It just appears when you do mathematics, if you're taking even roots of any numbers, right? Here's a rewrite of system talking about the plus and minus. The solution to x squared is equal to four is plus or minus two. You need both solutions to be correct. So you're saying, yes. I'm just saying we take square root of x to represent only the positive, because if you don't, it's not a function. Yeah, for sure. If you're talking about functions only, 100%, right? Function. And square roots having two positive outputs would make there be four numbers the quadratic formula would give us. Four numbers, it would give you two numbers. Like square root of, would be two values, wouldn't it? Yeah, check this out. Here. Now what system is saying is 100% true when we're talking about functions, right? So this comes into play here. Watch this. I'm going to kick it down for you. One of the first places we encountered this, right? Let me see if I got a pen that's going to be a little darker, better coming out. Is that better? Yeah, maybe. I need a whole new one. That's fine. Let's find a pen that's going to be nice and dark. That's not it. Let's dump that one. Oh, it's not bad. Brown, we use brown. There, we'll keep this one here. Let me see the red one too. Oh, that's nice. That's darker. Let's use the red one. Okay. Now take a look at this thing. Talking about why a function would not be a function or a relation would not be a function if you had a positive and negative outcome when you took the square root of a number square root of function, right? Now, one of the things that happens in mathematics is we try to manipulate functions, change things around to see what happens to them, right? So just imagine, just imagine you had this, y is equal to x squared, right? Let's assume we wanted to graph this function, right? Now, graph of this function is a quadratic. We've done a lot of quadratic. Or you could just create a table, right? So let's just create a table, right? Just so for those that want to follow what's going on here, you don't have to know about quadratics and the quadratic formula and completing the square and stuff like this to be able to graph this. So this is just a function, right? A function is just sort of a relationship with a special type of relationship where for a given x, you can only have one y, right? For a given input, you can only have one output. And right now, we have a y is equal to x squared and the x we consider to be our independent variable, it's our input and y is our output, right? So if we want to graph this function to see what it looks like, all we've got to do is put in an input and get an output, right? Put it in, get it out. So let's put something in for x. Let's put in zero for x. And all you do, you say, okay, y is equal to zero squared. What's zero squared is zero. Okay, so that's a point on the graph, zero, zero. Let's put another input, one. When x is one, we get one squared, we get one. So when x is one, y is one. x is one, y is one. Let's put another point, x is two, right? Well, if you put two for x, you get two squared, that's four. So when x is two, two, three, four, right? Oops, let's graph this better. So we're here. All right, let's put in three. When x is three, you get three squared, you get nine. That's four, five, six, seven, eight, nine. We're up here. We're off the board. So let's just graph this, right? Here's what it looks like on this side. Goes up like that, right? Well, okay, we've got a feeling for what the graph looks like on this side of the y-axis, right? Because this is your y-axis. This is your x, right? That's where your x, x this way, y this way. Well, let's see what it'll be if x is negative one. What's y when x is negative one? So you plug in negative one for x, right? So you're going to get negative one squared, which is one. Oh, one again. So one. And if you plug in negative two, you're going to get negative two squared. You're going to get four. Oh, so that's a mirror of that, right? Cool. Hopefully that's symmetrical enough. Symmetrical enough, right? So that's a graph of your base quadratic function, which is the parabola, which opens up like this. Cool enough. Now, what do mathematicians do in their infinite insanity? They go, hey, what will happen if we switch the x and the y here? Switch them up. Switch them up. What do you mean switch them up? Well, make the y and x and the x or y. Why? For the hell of it. Let's see what happens. Okay. Let's do it. So what happens if we do this? Fine. I want to do a different color, so we know it's the different stuff. Green, brown, fine. Take. Oops. Take. I don't want to write all capitals. Take inverse of y. Here. Take the inverse of it, which means flip the x and the y around. So what you get is x is equal to y squared. Flip the x and the y. That's what an inverse means. What it also means is a reflection about the line y equals x. So you're reflecting a line. I should make this one. Give it a little curve, right? Because it is a parabola, after all. Give it a little curve. Give it a little curve. So when you take the inverse of a function, what you're really doing is you're doing this. You're taking a function and flipping it about the line y equals x. y is equal to x. Okay. You're flipping it about that line. So okay. Let's do a little algebra on this. Well, if you're going to do a little algebra, you're going to get y by itself. y is your function. y is your independent variable. x is your dependent variable. Oh, sorry. y is your dependent variable. It's dependent on x, so you want to get y by itself, right? So you take the square root of both sides. So y is equal to square root of x, right? But what we talked about was square root has to be plus and minus, right? So square root of anything is plus and minus. Now, remember, we don't have a number in there yet, right? So do we have to write in plus and minus here? Not really, because we haven't taken the square root of x yet, right? It's just a variable, right? By definition, you take the square root is plus and minus, right? So let's leave it like that. Let's not put plus and minus there. Okay. Now, if this is what's going on and you're taking the inverse of this function, which means you're reflecting about the line y equals x, which means all you're going to do is flip the x and the y as you're switching the numbers, right? If you're going to switch the numbers, let's graph it. Let's create a table. Well, if we're going to create a table, all we're going to do is flip these guys. So the x becomes a y, so 0, 1, 2, 3, negative 1, negative 2, and the y becomes an x. 0, 1, 4, 9, 1, 4. Okay. We can test this if you want, right? What's the square root of 0? Put 0 in here. Well, square root of 0 is 0. What's the square root of 1? Square root of 1 is 1. What's the square root of 2? Well, square root of 2 is just square root of 2, right? What's the square root of, oh, I'm putting this on the wrong way. The square root has to go here. So over here, y is equal to, no, no, that was correct, y is equal to square root of x. So square root of x is equal to 1. Square root of 2 is equal to square root of 2. Square root of 3 is equal to square root of 3. Square root of negative 1. Oh, no, no, I'm already putting the, here, square root of negative 1. Square root of 1 could be negative 1, and square root of 2, square root of 4. Look at this. Look at this. I'm messing this up. 4 is 2. Square root of 9. Did I confuse guys enough? Square root of 1 is negative 1. Square root of 4 is, can also be negative 2, right? I don't usually do it this way. I'm trying to push it, right? So square root of 4, you put 4 in for x. Square root of 4 is 2, right? But it's not just 2. It's plus and minus 2. So instead of putting minus here, I'm going to put it here. Plus and minus, right? Square root of 9 is not just 3. It's plus and minus 3. Square root of 1, while it was 1, and negative 1. So it's plus and minus 1, right? So we don't need these bottom guys. We can just take them out, right? I hope that's clear. I sort of mucked it up in the process, right? Crafter, how you doing? Hope you're doing well. So check this out. What does this mean? That means, if we're going to graph this, when x is 0, y is 0. So we're here. When x is 1, y is plus and minus 1. When x is 1, y can be here, or it can be here. When x is 4, 3, 4, y can be plus and minus 2. Here, and here, right? And then 9 is plus and minus 3. We're off the board again, so let's graph this. Are we snagging anything today? I got some grapes. They're pretty good grapes. I got some that are loose here. They're really nice grapes. Just a little. I had a good breakfast. Let's see our grapes. I'm just going to focus on my grapes. There you go. Really yummy grapes. Oh, I'm going to look like it's got a little well done. Oh no, it's just the end of it. Check it out. So it's pretty yummy. As well as learning how to calculate my hand. No, I would not recommend. High definition grapes. High definition grapes, right? So take a look at this thing. This is what the inverse means of this function, right? Now remember, I keep on calling the function, but you can think of it as a relation, if you want. So if you take this function, this relation, and take its inverse, that means switch the x and y around, switch the x and y around, means you're taking this function and flipping along this, you get this. Now here's where the problem comes in, a system saying the plus and minus. If we say this is a function, then its inverse for it to stay a function means that it has to pass the vertical line test, which means for a given x value, it can't have two different y's. For a given x value, x is equal to one. It can't have plus or minus one as an answer. For x is equal to four, you can't have plus and negative two. You can't have an x pointing to two different y's. That's what it means for it to be the definition of function, right? If the question was, this is a function, then you have to decide if you're going to kill the top or kill the bottom of this, depending on your system. Usually you kill the bottom, and you say, oh, which means you're killing all the negatives, oops, all the negative values. Which means the inverse of this function is going to be this function, and this function looks like that. So you don't have the negative results when you take the square root of a number. However, if I set find the inverse of this relation, then if I define it as a relation, that means this can be a relation. That means the negative numbers can remain, which also means that these numbers would still be there. So it's all about definition. It's all about definition. Usually in high school mathematics, you're dealing with functions. So you end up eliminating the bottom. But let's assume you have this. Let's see if I was green pens doing. What if you had this? y is equal to negative square root of x. If y is equal to negative square root of x, then your graph would no longer be the top guy. It would be the bottom guy. Because the square root of x, you would define to be positive, and you're taking the negative of it. So that part would be the legit answer. Okay. Does that clear things up? Is that okay, system? Or anybody else that's wanting to know what this is about, right? It's interesting. It really digs down deep into the essence of what it is that we're doing, right? Most people don't appreciate this. And system, thanks for bringing it up, by the way. It's important to have a visual of what it is really that we're doing and why it is that we're doing it, right? How does the syntax work? And it's all about the word, right? Function. Function. Oops. Function. y is a function. That would mean take inverse of y, which is a function, right? If I say this is not a function, whoop. Or if you don't specify, right? I think it's legit to put it that way. It really depends on the teachers as well and the correction on it. Like, that's the kicker with this, right? It's really dependent on how you're learning it, right? But the syntax, the math, it's just there. It's just there. That's the thing with mathematics. A lot of, unfortunately, they make special rules in math to apply it to a certain system. And people think those special rules are universal and you can do that in the language of mathematics whenever you come across it. But that's not true because that applies only to that system, right? So, for example, when you're doing calculations, if you're finding maximum area in general, your graphs for maximum area when it's quadratic, you go from here to here, right? You end it there, your domain and range, right? Why? Because you're still solving for quadratics, but you can't have a negative area when you go down this way, right? You can't have a negative area, so you eliminate anything below the x-axis, okay? Because you can't have a negative value for that, right? That's the definition of the system. However, for quadratics, you can have negative numbers, right? That's their infinite, okay? I hope that helps out. I love talking about this stuff because it gets into the nitty-gritty of what it is that's going on, right? Nice chill stream. I like it. Little math talk is a good place to be. Yeah, I get it. The inverse relations certainly both positive and negative results. I was simply trying to emphasize the importance of the principal square root as it's called. Is it called the principal square root? Principal square root, okay? I was just pointing out that the square root used in the quadratic formula is meant to be a function and assumes just the positive values. The plus-minus comes from elsewhere. Not necessarily a quadratic function, but yeah, I appreciate, by the way, the system. I didn't mean to pound on your statement. I know what you were trying to get across, and 100% legit. I just like building on it, so I sort of use what you pointed out to build a little bit deeper on that thing. Little p, thank you very much for the following. There was a couple other people that followed. I saw the zombie pop up. Someone's been mentioning, well, we've been talking about it for a while, to change the zombie to something else, but we haven't got around to it. With the system, thank you very much for bringing that up, because it is an important distinction, right? Some people, unfortunately, you probably know, because you know this, right? There's a lot of people doing a lot of mathematics in school that they really don't know what it is that they're doing. They just get something to say, this is it. But what is that? Right? No worries. Unlike wise, happy to talk about it. Awesome, awesome system. And it really gets down to the nitty gritty of it, right? What's really going on? Yeah, you have to understand the definition of function to realize that, oh, you eliminate the negative part. Otherwise, it wouldn't be a function, right? And people are like, what do you mean? Well, that's what it is. That's the definition of it, right? It's like giving a range, giving a domain, what something can or cannot be. Fun. Right now, it's crazy. Right now, spring break, by the way, gang. So I'm assuming there are too many people doing a lot of mathematics. I have half of my students, no, more than half of my students I'm still working with. There's a couple of students that we reduced a little bit. One of them we took a week off, because I do private, right? I'm not in the system. So I teach math. I think math is math. Every day is math day. Whenever you can do math, you do, right? I agree. There's no use in shoving a definition down someone's throat without motivating it and understanding why we define certain things indeed, right? And by the way, gang, the reason we talk about functions is important, right? Because functions are about being able to make predictions, right? So when we're talking about functions, it's extremely crucial in our world. So for example, one of the things that I use to explain functions to my students is this, right? Just imagine if you're driving a car. Some of my students drive a car, some don't. And I usually ask them, do you know how to drive a car or what the principle is? They go, yeah. I go, okay, what happens when you sit in the car, put the keys in the ignition, turn on the car, right? And put your car in drive and put your foot on the gas, right? Some people say the car moves. Some people say the car moves forward. That's the distinction between a relation and a function. Those that say the car moves, they're defining it as a being a relationship. Those that say the car moves forward, they're defining it as a function. Because if they say the car moves, they're not specifying in which direction. Does it move forward, backward, left, right, up, down? Well, if it moves forward or backward, it's no longer a function because it's not predictable, right? It's predictable on those two planes, but it's not predictable per exactly what it's going to do, right? So it becomes a relationship. You put your foot on the gas and the car moves. It becomes a function when you can make the prediction that it moves forward. When you put your foot on the gas, the car moves forward. That is now a function. With that, you can make predictions, accurate predictions, right? System, also the difference between taking square roots of positive real numbers, all real numbers and complex numbers is important. Taking that, let me read that again. Also the difference between taking square roots of positive real numbers, all real numbers and complex, yeah, yeah, yeah. Once you delve deep into it, all the meanings of why certain things happen pop up, right? And those meanings have places they apply in the real world, which is super cool, which is super cool. Fun, fun. By the way, gang, I'm going to load up our Superman reading on, it's already available on bitchute and rumble, already let it loose. And it's going to be available on sensor tube after we finish the stream. Okay. So I'll let loose our Superman number 37 from number, from 1954 comic book reading that we did like four days ago, four or five days ago on Twitch. I'm letting that loose today, most likely today anyway. It's an interesting read, very historical piece. Right after World War II, a few months after World War II had ended, Superman number 37 comes out, right? And we did a reading of it. It's interesting. It was a good story. Interesting stories, right? Does the American education system make people learn formal logic for mathematics in general? Nico, Nico, American education system, neither the American nor the Canadian education system teaches thinking in school. They teach obedience. Okay. So system make people learn formal logic for mathematics in general. They don't really, it's horrendous here. Like, there's, you can't even discuss it on that level. So sad. So sad. Crafter, one thing I really miss in high school is real proofs. Yeah. We saw a few, but barely any, barely any, barely any thing. Barbara, thank you very much for the Twitch Prime sub. I don't think so. System says I don't think so regarding the formal logic. I don't think they teach any logic or set there. They don't teach, yeah, system, they don't teach any of that. And Nico, really the processing, the problem solving of a lot of students, kids coming out of university, coming out of high school, leaving university is atrocious, atrocious, especially in terms of mathematics, logic, right? It's very emotion driven, because with emotion driven curriculum, indoctrination, you can control people any which way you want. You can, you can, you can do anything to a society if you indoctrinate them into an emotional state of reaction, right? It's crazy. Crafter, now university, my classes are basically definition proof, statement proof, definition proof. That could be good crafter, it could be bad, right? System, crafter, same here. I love and hate it for different reasons. That's system. We're on the same page. It could be good. It could be bad. It's a love and hate relationship. Dingbobber, teacher, do you think the Rothschilds and other leaders who create the world education system work? Dingbobber, we can't talk politics on these math streams. Let's just say our centralized education system is horrendous, horrendous. We can talk about the politics of it in the future. I want to make sure the math stuff goes on sensor tube. If we've done mathematics, if it starts off going down a road that we can't discuss on sensor tube, then so be it. But if we've already done mathematics, I'll keep it strictly mathematics, because it's important to make sure as many people as possible have access to this information system. Some of the teaching isn't done super well. No system. I say horrendous. I don't think crafter. I don't think there's any country that really teaches formal logic. I don't know. I've had some students that are from international students that are pretty good at it. My bad Dingbobber says I might be wrong. Russia, like really the mathematics level coming out of Russia and some of the Eastern European countries and some of the like Iran, the mathematics level of those coming out of Iran is through the roof, right? Like you can't. Those students come here and they go, what? You guys are teaching what? No wonder it's so messed up here, right? Peligo. I'm going to study philosophy at uni in England, Cubs September, and the course includes module and logic. Is that the same thing? And what is it? Philosophy, the mathematics of logic is Peligo is crazy. For me, it was ridiculously easy. When I went to university, I took one logic course through the philosophy department, just because I wanted to see what type of mathematics that we're teaching through that book part, because it was mathematics, right? I needed mathematics electives and I thought philosophy of logic, cool, mathematics driven, cool. And it was just truth tables. And the class was huge. It was like 300 people or something like this. And most of the people were having extremely hard time with this. And I was like, man, it's just like plus and minuses, multiplying positive and negatives. If you understand that two negatives multiplied together give you a positive and negative and a positive multiplied together give you a negative and positive and negative is negative and two positives give you a positive. Congratulations. You just did truth tables. It shouldn't be that bad. Just think of it as pure, just syntax. Don't try to get emotion into the philosophy thing. That's the kicker, right? When they go into logic, there's no emotion involved. It's just syntax of the language of mathematics. That's it. It's not linguistics. It's not language. Even though they use language to confuse people, right? Glifton. My understanding is that if there is one and only one range value for a given domain value, yeah, they could only be one Y for a given X, right? That's what it means. Your range is Y, defined as Y, and your domain is your X, right? System. Look at propositional logic and predicate logic. That's likely what you'll do. You have a function. You have a function. Exactly. Gift denied. Niko. Well, in the Netherlands, kids from the age of 12 are divided according to capacity and only the top .1% is taught formal logic in high school. .1%? A .1%? Really, Niko? That's it? Oh, that's sad. Crafter. International. At age 12. So sad. Crafter. International students tend to be those that went to international schools and those usually differ a lot from the normal schools. Ah, no. Not necessarily Crafter. I met a lot of international students at university from all over the world, and they were pretty powerful, and they didn't go to international schools. In the high schools, not necessarily. I've come across students that just moved here to Canada. They're not, oh, okay, I see where you're going with that Crafter. Yeah, I don't mean just international students come to a country, come to Canada to study, and then they're going to go back or something. I'm talking about international students, the people who have moved here from another country. You know, from Eastern Bloc, and Korea is pretty good in mathematics and Iran and stuff. Their mathematics is pretty powerful. I've been told a lot of people struggle with it. A lot of people might struggle with it with a philosophy of logic, right, if they're not from the math department. Anybody who's studied mathematics should not have a hard time with philosophy of logic. Just learn the basics of the syntax of the language of mathematics, like how to multiply and solve equations and stuff. I had a teacher in college on tenure who would literally show slides, barely summarize, and skip to next slide, then sit down and let us figure it out ourselves for the rest of the class. Other teachers in the program were great, but not him. Yeah, I've had some horrendous teachers as well then, but I know that are believed to have better curriculum, like Russia and Iran, but those also don't do that much better on those piece of tests. The standardized tests are not testing your ability to do mathematics. They're testing your ability to how well you know the language that you're being tested on and how you can solve problems that shouldn't have been problems to begin with, right? They're basically psych analysis. They're not analysis of how well, how intelligent somebody is. They're personality tests, really. They go, oh, cool, thanks. Seems to be that we overcomplicate things, and perhaps people are overthinking it. Yeah, yeah, indeed. People overthink it, right? Because when you say it in a certain way, because people are just saying it in language, they think it means this, but then if you break down the language into or quantify that language, it means the opposite, right? Niko, yes, it's not in the official curriculum, so only the mathematics inclined students of the gymnasium schools are given the option, and most of them opt out of it, huh? It might be slightly higher, but anything between 0.1 to 0.5% seems a good estimation, really. That's not very many. My theory is people should be being taught mathematics on a very higher level than they are right now. Our societies would be better off for it. I know people are saying, oh, everyone doesn't need to do mathematics. Everyone doesn't need to do this. It's like saying everyone doesn't need to know how to read and write, right? Everyone needs to know how to read and write, and everyone needs to know how to read and write mathematics, okay? And Belgium too, crafter, right? Ding Bobber, my biologist friend recently bought a 11,000 Canadian supercomputer with his professor, who he works under. The process, to process data and use machine learning, impressive stuff, impressive. Maybe they bought it to mine some cryptos, and they're just saying they're doing it for that. Taxpayer-funded crypto mining machine, but an estimated higher 2% in Belgium that would get taught logic, damn. Supreme Leader of Twitch, hello, hello, how are you doing? And gang, don't forget, free Assange, free Assange, free Assange. Julian Assange is a journalist and publisher that has been crucified for trying to bring transparency and accountability of capitalist power to humanity. For more information, see wikileaks.org, defend.wikileaks.org, or our Julian Assange and WikiLeaks playlist. Those who usually go to study math or go into engineering or physics, only 1-2%? Damn, I don't know, I'm biased. That's not enough. Ding Bobber, ah, yes, probably. Nico, well, 6% goes to a gymnasium, and a quarter of them is math mining client, only one-fifth of them off to take it from my experience, okay? It depends on some of the electors, like, when I took philosophy of logic at university, you did gigantic truth tables and stuff, and you solved certain problems and stuff, like, really, I found it ridiculously easy. Maybe it was just a mindset I was in at the time. It was a first-year level one, though, so it was it was really geared towards the easy front. Again, I'll say this again, learn math. If you're struggling through it, kudos on you, making yourself stronger, you're building your neurons, you're making them thicker, they're firing, right? It's like going to the gym and lifting weights, you get tired, you get sore the next day, you got to eat well, you got to rest well, you got to do it again and again and again, but when you do that, you get stronger physically. If you study mathematics, learn the language of mathematics and how to apply it in your world, you become smarter, and not just smarter, but wiser, okay? As you experience more of life and process more data, more information, and use the language of mathematics to improve your life, man, math makes you smarter, you can't lose, learn it, right? Xenos paradox. I forgot what Xenos paradox is. Crafter, we had formal logic in first semester, but we saw predicate logic, truth tables, electoral boards, electoral boards, I don't know what electoral boards are. We saw how to make some adder, I guess that might not be formal logic anymore. I don't know, I didn't take it beyond that one course, I just didn't like the direction it was going, right? It was just, I wanted more hardcore, gift or not. I think Xeno was on to something, the universe manifests the infinite instant, infinite instantly. It's amazing, even though it doesn't disprove motion. So everything, so Xenos paradox, I gotta look this up, what is Xenos paradox? I want to read this thing. Electoral boards with the and, oh, and, or, and, or, yeah, yeah, yeah, yeah, yeah, that's what they're called. Electrical boards, yeah, yeah, we did those. Those were trippy, they just, they were set to confuse people, but then once you understood what was going on, that they're trying to confuse you, then it just became easy for me. I just had to appreciate what it was. So Xenos paradox, I'm just going to read this. I don't know why I'm reading it through Wiki, but why not? For non-political stuff, this is okay source, for mathematics is okay source. Xenos paradox are set of philosophical problems, generally thought to have been devised by Greek philosopher Xeno of Ilya in 490 to 430 BC to support Parmyndias' doctrine that contrary to the evidence of one's senses, the belief in plurality and change is mistaken, and in particular, that motion is nothing but an illusion. It is usually assumed, based on Plato's Parmyndians, that Xeno took on the project of creating these paradoxes because other philosophers had created paradoxes against, for instance, the view, I would have to look into this further. The paradox, Xenos paradox, fun game. I hope you have good snacks. I'm going to pop a couple of more grapes or one more grape anyway. He was fun, was he fun? A lot of that stuff, the philosophy stuff, is super cool to play around with. Your popping grapes is also called nice. Slowly we get into grape season. Oh man, can't wait for fruits, fresh fruit to come in. He would use logic to make people's second guess, no one maligns Xeno. Also called effin with people, right? Fun, fun, fun stuff. It's just messing with people, right? Have you ever done that? Have you guys ever messed with people just to mess with them? Sometimes fun, don't be mean, just be fun, right? Just be fun. But in times of chaos, it's best to be straight up, right? Otherwise, you might be, you know, find yourself in some hot water, which you don't want to find yourself in, right? Oh, of course. Glyftenoid, glyftenoid, fun, there's a good name by the way, glyftenoid, I hope I'm pronouncing it right. Fun. Have you ever worked with Iranian students? Yeah, yeah. I have one here, I'll give you an example. I have one Iranian student come to me. It was about two and a half months before he had to graduate, right? This is grade 12, right? He was he was related or a friend of a friend's a friend's friend's sibling, right? That was still in school. So he came up to me. He called me up said, hey, Chicho, you know, I'm so-and-so blah, blah, blah, blah, okay, cool, cool, cool. And then he goes, by the way, I'm in grade 12, graduations in two and a half months, or let's say three months. It was three months under graduation, and I need math 12 to be able to graduate. I go, what? He goes, I need math 12 to be able to graduate. I go, so you need another course to be able to graduate and it needs you want it to be math 12. He goes, yeah, I need the credit to be able to graduate, and I need math 12 to be able to get into a program that I want to get into. I go, okay dude, up to you, but it's really quick. You have to do exactly everything I say, and it's your schedule, right? He goes, okay, I go, well, do you have the material, the booklets? Like this was long time, it was 18 years ago or so. He goes, I go, have you applied to the correspondence? Have you got have you have the course material yet? He goes, not yet. I go, dude, apply for it, get it. So it took him two weeks to get the material. He came to me two and a half months until end of the school year. So we took the course material and I went, okay, taught him, do this, do this, do this. And every time I would teach him a lesson and tell him to do this, right? I say, okay, as soon as you're done, send me a message and we'll have our next session. Okay, I'm not going to, I'm not going to see you on a set schedule. I'm going to see you as you process, learn the material, right? And he goes, okay. So every now and then he would go do it, not every now and then, more often than not, he would go do it that night and then send me a message in the evening or the next evening and say, okay, I got it done. Can we have another session? So we do another session. We got Math 12 in Canada, Western Canada. And at the time, Math 12 was a way higher level than it is now. Like they don't do conics anymore in Math 12 here. They don't do statistics anymore. So just imagine Math 12 curriculum 18 years ago had a chapter on conics and a chapter on statistics. That would have been about minimum three months out of a 10 month course. They took that out, right? And they've taken that other stuff out. So that stuff was in there as well. And he ended up doing it. We finished it in two and a half months. And he got like 92% on it. And you know, off you go into the world. Good boy. He did what needed to be done. And he got it done. It's easy to do if you set your mind to it. Okay, you need the foundations. You need the foundations. And that's the kicker. They're not teaching the foundations at elementary school. So kids are coming into high school thinking of math hard. And it's indoctrination, programming. It comes from mainstream, like consumption as well, right? There was, for years, there was a Barbie doll that said, oh, math is hard. You press the button and the Barbie said math is hard. Math is hard. What the F? I can honestly tell you, the students that I've worked with, there's girls that I've worked with that are, they can learn math like this. They are crazy fast math learners, right? On average, faster than the boys. They process it, right? But there's some kind of stigma attached with people saying math is hard, right? And I try to get that out of them, right? It's like, awesome. I missed a chunk there cooking, but seems to be some great quadratic grass here. And the inverse. And the inverse. Gang, what should we do? Should we call the stream? Cheecho the mad wizard? Putin, roaster, how are you doing? I haven't seen you for a while. I hope you're doing well. Fun, fun, fun, fun. By the way, has spring kicked in for you guys yet? Spring's kicked in here. Summer time's coming. Summer time's coming. Spring, we're into spring. First day of spring, second day of spring, right? Fun, fun, fun. Fresh fruit coming. Start eating fresh fruit as it comes. Spring is here. Insect spotted already. Insect spotted already. Ags, how are you doing? Our last snow melted. You're still had snow? You had snow until like recently? Wow, axe. Yeah, my allergies are really bad. Oh, your allergies have already kicked in. Dang. Dang. So we got people from two different parts of the world, most likely. Axe, where are you from? Putin, where are you from? You guys just had your axe. You still had snow on the ground? March. It's a march. It's still a little bit cold here, so I haven't gone out on a patio to plant stuff. Sweden. Oh, Sweden next. We had some snow coming down last week. Dang. Sweden. You guys were like Canadian weather. If you're on the coast, I'm assuming you don't have that much snow in Sweden, in the southern part anyway. For us, we haven't our snow disappeared a while ago. Still getting to four or three degrees, and you can have ice forming at four degrees Celsius. It's weird because at zero, ice forms and melts. So at zero, water can turn into ice and ice can turn into water. At four, water can turn into ice as well. It's called getting, what do you call it, black ice on roads. It's thin and it cools down just enough to hit that. When it's four degrees outside temperature, so it would have to hit the zero mark for it to become ice. Kurosh, you're Iranian. Would you hold a session talking about derivatives in the future by any chance? I'm really struggling with it in the last year of high school. The topic is single-handedly ruining my math career. I really enjoy studying with this stream, and I'd assume it would be easier for me to learn derivatives this way. Yeah, Kurosh. We did. I'm not touching calculus too much, but we did do a session where we did here. Let me find it for you. Because I've had a lot of people want to learn calculus for me to teach on calculus, right? Oh man, where is it? Where is it? Shoot. We just did it recently. Oh, here we go. Check this out. Found it. Found it. Found it. Found it. Found it. Is this one going to be it? Yeah. Calc-1 graph, graduate function. I think this is the one. April, maybe. April, that was last year. Maybe there's better ones, but check this one out. This sort of touches on it. This touches on it. Let me just go to my drop in math tutoring folder where is it hey I might have a better one than this by the way let me find it let me find it because the next session I'm gonna do is gonna be a couple of weeks from now so I do want to make sure that you do have what you need so let me find it and then I decided to do a full-blown like intro to calc here's our my drop in math here I'll link this up to drop in math playlist on sensor to Matthew redeem 500 points thank you for redeeming five other points fundamental theorem of calculus find the derivative there we go okay we open this up grabbing functions oh here's another one what is calculus cubic functions systems of equations yeah there's a bunch of calculus stuff here here's another one fundamental theorem of calculus this one goes through the fundamental theorem of calculus okay lays it out for you Grosh let me know how that stuff helps and we do have a discord page and we do have a mouth mouth folder there this court you can pop in there and in the heavy topics there's a math folder there so there are some people that do help people out in that folder if you have questions this has been such an important stream slick mix size when and of you upload this on bitchu I'll be watching it regular awesome slick mate thank you so much my pleasure Kuroch I'm sure it'll help a lot I hope so if you have questions let me know and there are other times where I've hit it up I don't know if that's the one that I went through the beginning from beginning to end I might have done another one I might have done another one aside from that gang let's call the stream okay thank you for being here slick make thank you for the questions system thank you for an engagement thing bobber everyone thank you for being here thank you for the follows thank you for the subs thank you for the discussion it's a lot of fun if you want to know what this work is about I am on patreon patreon.com forward slash chico ch y ch o if you want to support this work if you want to follow this work this way patreon is a good way to do so okay everything I do is basically layered on mathematics I don't put anything behind paywalls everything's creative commons share and share like for those of you that was supporting this work on patreon thank you very much for the support gang it is in large part because of your support that we're able to do this we are live streaming on twitch twitch.tv forward slash chico live ch y ch o l i v e and again gang thank you for the follow us thank you for the subs thank you for being here thank you for the discussions and to our mods thank you for taking care of business we do announce these live streams 30 minutes before we go live on parlor vk mines and gap you can follow the work there and you can come to our twitch channel anytime you want and in the chat if you type an exclamation mark social all the links to those platforms will be there including our discord link at the bottom there and you're definitely welcome to join our little community of a few hundred people to discuss whatever you would like thank you for the stream so my pleasure kuro shi my pleasure and good luck with the calc for last streams that we don't have any visuals we do upload the audio to soundcloud.com forward slash chico ch y ch o is a podcast and that should be available in your favorite podcasting platform including spotify my things I haven't seen the schedule anymore today or tomorrow tomorrow tomorrow we're going to do chico salvia the normal chronicles and on wednesday we're going to talk personal finance this is the this is the ninth live stream we've done the last like 10 days so we're doing an 11 live stream set basically it was a nine live stream set and we did two unscheduled live streams so we got two more the next two days one tomorrow at 10 a.m. chico salvia the normal chronicles and wednesday evening i believe at 8 p.m. pdt my time talking about personal finance investing in personal assets they can all be there awesome should be fun and gang we will be uploading the stream to sensor tube to bit chute and to rumble and if we get enough points once that kicks in onto odyssey as well and you can support this work on those platforms by liking sharing commenting and if you're on sensor tube you can support this work by joining sensor tube you membership there's a button there and there is a handful of you that are supporting this work on that platform gang thank you for your support it is because of the collective support we're getting on these platforms through you that we're able to do what it is that we are doing and we appreciate it very much i hope you have a fantastic day and if you can make it we got two more days of live streaming going on and superman number 37 reading being released today most likely on sensor tube it's already available on bit chute and rumble from 1945 buy them oops buy everyone scared people scared me