 wait until I see it coming on Twitch. Welcome everyone. We're at the end of school year 2018 in the northern hemisphere anyway. Not sure how it works down south I think switched up a little bit. So basically I thought we'd do a couple of days of math for anyone interested if they have questions, if they're cramming for exams, if there's anything they want to work through or understand better because I you know for some of my students, for some people anyway, school marks matter a lot because it's their you know sort of the stepping stone for them to progress to post-secondary education whatever it might be or whatever they need to do to continue with their work right. So hello Hannah, how are you doing? I haven't seen you for a while. Welcome, welcome for the mathematics. Hey Casey, how are you doing? Just popping in for a wee while to say hi. Thanks for popping in brother. I saw your comment by the way regarding Aaron Schwartz's documentary. I was following that stuff from the get-go. I've been active on Reddit since it was like really just at the beginning stages and I was following what happened to Aaron Schwartz and and the platforms that we used to share information stuff like that and how they've been hijacked, taken over and what happened to Aaron Schwartz and stuff. So I made a comment saying on Discord that if I need a little motivation to do some before political stream or something like this I might watch that just to get my blood boiling so I can be a little sharp in the strings or whatnot right. But thank you for bringing it up. I've seen a few other ones docs about open source community creative commons, the different types of things, right. My fave, Chicho is the king of yes so far. Having fun with it, right. Having fun with it. Yeah and again this is going to be sort of open discussion. We're open to do math basically. I know it's at the end of the year and someone commented when I did the announcement saying that we're gonna do mathematics. Someone mentioned that the year is already over for that so I guess they finished early but I'm guessing they're probably in college or university because colleges and universities finished school earlier than high school and elementary school in my part anyway. So in my area right now what's happening is all of high schools they're basically an exam period in the second week of June. First week of June, second week of June, they're going to exam period all the way all the way through June. Some people write exams at the end of June as well. So I thought I'd give people an opportunity to you know if they have any math questions we could do. I might do lessons or whatnot or it'll just be an open discussion. I'll just hang out and whatever you guys want to talk about we can talk about if there's no one into doing mathematics, right. They might have already all everyone might have already packed up to to go you know to do whatever it is that they're doing. I know and it's sort of changed from when I was in high school just to give you a little bit of info. Basically to get accepted into university in the past when I was in high school in the 90s could you please review the chain rule for my oh I'm not touching calculus and I'm sorry I got to review my calculus. I have to review my calculus and relearn a lot of the stuff because I haven't been teaching it or using it. Yeah I know it's all good for sure but I've had a lot of requests to do calculus really more than I was expecting to have the truth. I wish I was getting more requests to do statistics because I think statistics is more broad, reaches out to a lot more disciplines. So I've been touching up on statistics a little bit but I should have been touching up on calculus to be able to do calculus right but promise in the next year or so once my workload sort of transfers over to the online versions that have anyway once I balance things out a little bit I'll try and get on that calculus and start creating some content for calculus. Calculus and stats are amazing very challenging but so applicable in real life it blows my mind yeah 100% and unfortunately they don't really talk about that teach you that in school they mention it but they don't really cover any type of content material that the kids are interested in which is a shame right because they just assume mathematics is not applicable that's useless for them and they move on doing other things and at some point in people's lives they come across a hurdle or something they need to learn how to do or do for their company or whatever it is and it's all mathematics and now they have to relearn everything right hello valiance how are you doing hey chichou been a while since I have been able to drop by no worries brother no worries brother I'm gonna be doing this for a long time so there'll be a lot of opportunities to drop by the live streams definitely definitely my biggest regret in my schooling is not taking math and science more seriously when I was younger I was very immature in middle school yeah that's the case with almost everyone and I don't you know what I wouldn't I don't know your particular case Anna but I wouldn't say it's because of immaturity that a lot of students a lot of students don't take math and science more seriously I think it has to do with the way our society is structured and the amount of distractions and noise in our communities that and a lack of sort of I don't know if you associate that with the maturity but lack of discipline and lack of lack of understanding what it takes to really be able to function in this world right it appears to me anyway almost everybody is is growing up in a bubble in the Western world they think the world is the way they perceive it to be they don't appreciate that the world is a lot different in general then what their experiences I have taught them up to the point wherever they are especially in high school right there are a lot of kids that are really worldly wise and stuff like this but it just doesn't all come together which is very very unfortunate very unfortunate a lot of people a lot of kids are gonna get burnt I just found out through one of my students and this is you know I was working with them I am baseball I'm a baseball coach and I tell my players school specifically math it's the mastering mastering it's like master in the sport you got to do it nearly every day I take the time to get reps in you either use it or you lose it yeah that's one of the things that I learned from someone else but we're talking about something else other than mathematics but they always said use it or lose it baby so yeah you either for me like I knew calculus I knew statistics well but I haven't been using it so you know if we're teaching anyway I use a little bit in some of my work that I do especially when I'm looking at stats of the streams and that videos and processing some stuff and looking at trends 100% but not on a sort of academic level right so you do if you don't use it you lose it and sports is a great way to it's a great analogy and one thing I do with a lot of a lot of students I have that do sports and it's incredible when it comes to mathematics a lot of people assume that those who do who are athletic are gonna be bad at mathematics right I've had students that are you know top either football soccer rugby but basketball players and the team right and a lot of people have written them off over the years regarding academics but then once I started working with them and they learn mathematics all of a sudden there's a certain way of it especially with sports those who excel in sports they like to tackle they like to go head on into a situation if they're you know a team sports anyway if they're competing this other teams other other players right they go head on into a situation so if people teach them mathematics science in that way the athletes tend to pick up the material a lot faster I've had some some top level kids who are into certain types of sports that didn't excel in mathematics or sciences when I started working with them and by the time they reached grade 12 they're taking you know they're acing their mathematics and they're doing phenomenal in science is going into engineering right but the school doesn't teach them that if they a lot of a lot of schools because they get a lot of money for participating in sports they get a lot of prestige what they do is they push the athletics at the sports aspects of the system right they sort of you know I might be being a little harsh but they really use and abuse their students right they they put them in a little bubble right they take all they can from these students excelling in whatever sports that they're excelling in but they drop the ball names and everything else so when the kids are done with school they're done with their athletic career if you want to call it that they're left out how out to dry right they don't have any safety netting anything to fall back on right and that's when they get into depression and you know they're they're prone to fall for any scam that comes along hello Malik how are you doing it you show and chat agree with your assessment for many people that is not important how things work only that they do work yeah yeah it is good to connect up there some of the reasons some of the some of the what do you call it the stepping stones that they need to be able to appreciate understand what's going on but they just need to do right that's that's the way I've seen with a lot of my students for excelling athletics they just need to do right they just need to sit down forget about the proofs of things and stuff tell them how it works get them to do it they pick it up super fast and they don't forget they tend to forget they tend to retain the information a lot longer yeah thanks man been seeing a lot of chat on this court but haven't really contributed much recently either but I've been pretty busy with my students and stuff my brother was like that as mentioning he was a 3.7 a GPA student and now he is an honors architectural engineering student and Drexel you are possible awesome that's good that's good it's good to hear success stories and in academics make me really happy really cool the discord is bubbling along nicely it seems to boost around strange I bet it does on this court nightbots I'd like this nightbot thing I keep on mentioning it but I do like it it saves a little bit of time I should add on more stuff to it actually he often helped me with my homework good stuff siblings siblings is a funny thing some there's clashes and then there are some that are very tight just car zany a bat and a ball cost $1 and 10 cents in total the bat cost a dollar more than the ball how much does the ball cost the ball cost 10 cents a bat and a ball cost $1 and 10 cents in total the bat cost a dollar the case you might have the right answer five cents should we do this one we could do it how do we lay this out problems a ball a ball a bat and a ball cost $1 and 10 cents Casey knows bat and a ball let's let's do it let's do let's do the word prompt okay here let me do change the view okay and this is the view we're gonna use let's lay it out the way we would legit problem right so bat and a ball cost tense dollar and 10 cents how do I plan on pajama party for my grandparents the grand parents so I guess they wear pajamas either that or the ball is free bat and a ball cost $1 and 10 cents the ball cost a dollar more than the bat cost all more sure so let's do this let's do a let's statement let's be equal the ball and let's bat T equal the bat okay so a bat and a ball cost a dollar and 10 cents so bat or the ball plus actually let's put it in order the way we read it usually try to lay things out exact the way you're reading up to a certain degree right so bat and a ball so T plus B is equal to dollar and 10 cents and the bat cost a dollar more than the ball right so the bat the bat T is equal to the ball B plus $1 right so all you need to do is do substitution T is equal to B plus 1 right and that's the same T as this so what we could do is take this and sub it in to here right so B plus $1 plus B is equal to a dollar 10 right so this guy is this guy here right okay now all we do we combine our like terms B plus B is to be is equal to and we're gonna grab this guy bring it over minus $1 right so that becomes 10 cents oops let me write it down as decimals so that equals 10 cents and then you divide by 2 divide by 2 so the ball cost 0.5 0.05 which is 5 cents which is what Casey said right on Casey right fun I always get that wrong believe it or not whatever someone asked me that question right off the bat it's instinctive to say 10 cents but should think about it right I should think about it anyway did you eat it out of the ball is free yeah the ball should be free if you're buying it back I'm interested investing in some cryptos wondering where you get info in making investment decisions on some of the newer cryptos you have to go to your websites right and it's a dangerous game investing in new cryptos I think it's it it's legit it is it is going to go where it's going to go right the only way the powers that be can stop it if they criminalize holding cryptos and start going after people and throwing in jail which is something they did with prohibition right back in I forget what the date is but they basically meant they basically passed the law that said growing hemp you needed a sort of a number a tax number to be able to grow hemp industrial hemp in the United States anyway and they wouldn't give out that number the permit to anyone to grow hemp and farmers have been growing hemp forever right so they grew hemp and then the IRS came and I think I have my history correctly I read this stuff a long time ago they came in and anyone that didn't have the tax permit which was nobody had it because they didn't give anybody the right to grow hemp they threw them in jail like the first people that went to jail for because of prohibition because of criminalization of cannabis were white farmers right which is crazy so they could pull the same thing with cryptocurrencies they could say anybody holding cryptos you need to have some kind of permit to have it if you're trading it they could pass certain kinds of laws saying that it's I've looked into this stuff it's a currency and you know you're a currency exchanger and stuff like this some technical every word has certain certain type of meaning but right now I think the best thing that can happen with cryptos is to be classified as an asset right that way and I think that's where it's going with a lot of things and that's the way I look at it cryptos aren't really currency right now they haven't been currency since the prices went up and people started hoarding them right so cryptos for me they're sort of collectibles they're money right they're not currency their money and anything can be money we've talked about that right and basically they're assets so what you need to do is take a look at their websites take a look at who the people are who are involved with a specific type of crypto and really dig down and see if you you know have a good understanding appreciation of what those cryptos what those companies are doing basically they're they're providing they're doing IPOs but they're calling them ICOs right Michelle Cohen offers I sort of talked about this in the last cryptocurrency video we put together right and I think that's the way you have to approach it and really dig down into the history of the people involved with crypto right if you're planning on investing if you're just trading buying and selling follow the charts it's just charts okay sell the news buy the hype I guess if you want so play it as if it was penny stocks and do it that way but cryptos might be in for you know they might go to the moon or they might be in for a rough ride I personally wouldn't have a hell of a lot invested in cryptos or put into cryptos I'd be trading actively because the the rug could be pulled out from under them in an instant and they could also shoot up to the moon in an instant so if you're constantly trading taking 20 percent off the table every time you're ahead of the game that's my that's what I would do but that takes a lot of energy that takes a lot of effort right the main cryptos they're probably not going away right bitcoin ethereum ripple monero some of the other ones they're probably not going to go away their value might change will change okay I literally just finished the math exam yeah some people are writing their exams early it's weird five cents plus dollar five yeah yeah race kill is mentioning the ball and bat problem cool and I'm not looking forward to the results oh no I hope they come out okay regarding the test be right back what is going on on this beyond my comprehension what is going on I guess here beyond my comprehension we're doing math we're talking about life good evening master good evening good morning for me good evening to you and the legalize it Hannah says most definitely stop for my take any centralized authority that criminalizes anything is stepping beyond the we'll leave it that we're talking about math guys maybe we'll do a stream on prohibition and legalization once I collect compile some of the data that I've collected yes chicho spam a lot hello how are you doing and in lake there is a patch let's check this out let's check out the next question in a lake there's a patch of lily packs okay every day the patch doubles in size if it takes 48 days for the patch to cover the entire lake how long would it take for the patch to cover half the lake okay sure let's do that problem and by the way on this note zany just just I car zany just the car zany I think I'm just going to refer to a zany just on that note I was mentioning that I was working with a student that I have not the size of the patch equal one yep 100% you could definitely do that just regarding this growth and this is exponential growth I believe is exponential growth doubles in size yeah this is exponential growth someone's doing all the problems already we'll confirm those right we'll do it down here but I was working with a student a couple of days ago yesterday or a couple of days ago and they're in grade 11 right they're in grade 11 and for sequences series there's a chapter for sequence series that they've been teaching in grade 11 for at least two decades right it's been in grade 11 curriculum and they talk about arithmetic sequence series and geometric sequence series and they've been talking teaching arithmetic and geometric sequence series which are basically exponential growth it's sort of an intro to kicking off to exponential growth and kicking off to calculus and whatnot right they've been teaching this for about two decades as far as I've been involved with it right I just found out two days ago in a new curriculum they're rolling out in my area they took out the geometric series and sequences blown away I was blown away that they would take a chapter and cut it in half right and decide to take that information out of grade 11 mathematics and they're deciding to introduce it in grade 10 but as soon as they introduce stuff in a lower grade they're dumbing it down they've done this before in multiple other things or sometimes it's just completely eliminated so just imagine not being taught exponential growth in high school math right that means people have no concept of how our economic system works at present how population growth works at present they will have zero understanding of global geopolitics economics anything if they don't understand this blows me away uh z-chart question that's statistics um I can touch on it a little bit let's do the uh spam a lot let's do the question that was posted regarding the patch and then we'll do that when I was in Israel this past August I had the time in my life and I got a haircut for an amazing Armenian barber in the Armenian quarter of the Jerusalem the jennifilm was the nicest dude ever and gave me that nice haircut I thought of you when I got out hopefully they weren't bald maybe they were if I was in another life maybe I'd be cutting hair uh fun um okay so what was that question let's check this out so in a lake in a lake there's a patch and there's a lily patch every day the patch doubles in size it takes 48 days for the patch to cover the entire lake you said you were yeah I am Armenian descendant lies I am Armenian or you said you were Armenian yeah I was blood-wise I'm Armenian born in Iran most of my life Canada so I'm Canadian Armenian Iranian Iranian Armenian Canadian Armenian Iranian Canadian Armenian Canadian Iranian whichever way you want to call it right next time you're there tell them uh say barib to that barib in Armenian means hello so that was in size in doubles in size did it every day the patch double so every day the patch doubles in size it takes 48 days for the patch to cover data yeah the quick answer to this is uh 47 because the next day would double so it would have to be half so we don't really even need to do mathematics while we are doing mathematics but mental math right so let's lay this out let me erase let me change the camera angle your Kenner Armenian Kenner Armenian that's actually pretty cool I want to start calling it that Kenner Armenian citizen of the world I like to think I'm a human being citizen of the world I used to tell people in Babylonian and whatever it was right oops that's the wrong one this is the one that's the one okay cool looks like the green I have to erase faster so just imagine just let's do a visual of this right so here's a here's a pond right here's a lily patch right here's a lily patch this lily patch doubles every day right and in 48 days 48 days equals full right the pond is full of lily pads so how long does it take for the lily patch to cover half the lake well for to cover half the lake what has to happen is the next day it's going to double right so the only way the lily patch can double the next day and cover the whole patch if the day before it covered half the pond right if it covered half the pond then the next day it's going to double that means it fills the whole lake so it's 47 days right and this is this is a serious concept when it comes to exponential growth when it comes to our current economic systems when it comes to our political systems when it comes to the environment resources and stuff like this because right now this concept this type of problem should be emphasized more in school because right now what's happening is one of the best examples you can think about is I've heard this use a lot where if you have a like a milkshake or a drink and you're just drinking out of a straw right you're drinking you're drinking out of a straw and the straws let's say you have your glass and the straws all the way in the bottom right so you're drinking you're drinking everything's fine and dandy you think the drink is unlimited if you know let's say it's a blind sampling right you don't see how much liquid there is in the glass jar or the cup you're holding right so if you're drinking you're drinking everything's fine and dandy you're getting all the liquids you want until you get to the end and then you're dry you're done right that's the way the resource extraction is working that's the way the environment's working as for a formal way of laying this out how should we lay this out i haven't done one of these problems for a long time lily patch lily patch you can't even do this al actually we don't even know the size of this thing full you know what i would just approach this this way i would say this is the best way to approach this in 46 days i mean if you can take a look at this in 46 days right it would be a quarter full right in 46 days it'd be a quarter full because the 47th day would fill up this and the 48th day was full up this if that's enough for you might just leave it there because that's the best way to look at it sometimes mathematics is best done visually instead of laying down all the formulas and stuff like this the formulas and the variables and stuff that stuff is really good if you actually don't have sort of problems laid out like this if they give you variables if they give you numbers and you know exactly what you're shooting for okay i hope that's okay if you want to do more formal we can we'll think about it and do it let's check it out i just say i'm an ozimantius king of kings look upon my works you might despair i don't know what ozimantius is i'm gonna well done rescuer let's check it out ozimitius what is that word ozimitius is a sonnet written by english romantic poet Percy Bush Echeli first published in the uh in 11 january 1818 issue of the examiner in london it was included in the following year Echeli's ah that's cool ozimetius oh here it is persistent i met a traveler from an antique land who said too vast and trunkless legs of stone standing in the desert near them on the sand have sunk a shelter versus that's cool there's two of them in each of sandy silence all alone stands a gigantic lake not interesting i gotta get more into poetry i like hip-hop i like rap poor shochicho ozimetius is also a character from that's right why do we study only functions in school um why do we study only functions in school and not relations i mean the question is why study only functions and not relations in my part of the world they used to teach relations a little bit and they took that out and they just focused on actually they still introduce relations but basically the reason we study mainly focus on functions uh is because with functions you can make predictions basically the hierarchy the pecking order of things is this let me lay this out for you let me change the view again so basically are what we want to do with mathematics for us to use math in the real world to quantify things to be able to understand how systems work is this right we take something a certain type of system and try to formalize it like the the pawn one right we give you know we do let statements we say this equals that that equals this and stuff like this and we put things together like the ball and the baseball bat right we take sentences the way we uh think how things are related and we put them in an equation an equation usually is a sentence connecting up different variables different thoughts right and we end up doing this and we look at different types of systems and the most general type of system we have what we're trying to find out is we're trying to find out if variables have relationships right so what we have is this relation really am i spelling this right even relationships i think so let me let me check my spelling on this because i hate to spell this incorrectly yeah i think so okay sometimes i have brain farce i totally forget how words are spelled right so we have relationships okay and basically relationships are you know if one thing is related to multiple other things or if one thing can possibly be related in two different ways to to another variable right graphically relationships look like this right this is a relationship a circle for a given x value right you can have a y value or multiple y values right this would be a relationship right this is a radical this is a circle x squared plus y squared equals r squared or more generally x plus k squared plus y plus h squared is equal to r squared right where k and h the opposite signs of the center of the circle and r is the radius of the circle right so when it comes to a relationship a given x value can give you one or more y values right so for a given x this x value we can have two different y values which is useful right or multiple other y values okay but the problem with that is just imagine if you're sitting in a car you turn on the car right and then you put your foot on the brake because i usually there's a safety mechanism you've got to put on your foot on the brake before you can change gears or if you're driving standard right but let's say you put your foot on the foot on the brake right turn on the car and you put your car in drive and then you put your foot on the gas what's the car going to do right if you put your car in drive and you put your foot on the gas the car will go forward i asked this question this is a question i asked my students a lot right i go okay the difference between a relationship and a function if you sit in the car turn on your car okay and you put your car in gear you put your foot on the gas i had turned my students to say what is a car going to do more than half the time the students say the car is going to move right and then my reply to that is well is it going to go forward backward left right up down right when you put your foot on the foot on the gas and the car moves that's a relationship when you can make a prediction of which direction that car is going to move that's a function right and functions to us end up being more useful because we can extrapolate into the future and we can take a look at the past and try to figure out how we came to where we are right if for a given x value you have multiple y values let's say the function does this or the relationship does this right well for this x value here we have one two three four five different y values and this is things that happen in the real world right really this is situations that do appear in the real world but we don't know exactly which one it is for example when it comes to atomic structures right they used to teach us that this is the nucleus of the atom right nucleus we've got neutrons and protons and around the atom we have electrons orbiting right this is sort of your first introduction to an atom works but an atom really doesn't work that way the structure of the atom the structure of the atom is the nucleus here and there's probability you know i'm not sure if i'm drawing this correctly or not but there's a probability area where the electrons can appear right and if you look at them the probability is they're not there so you can say the electrons appear in these probability zones but you can't tell which direction they're going to go if i remember my chemistry correctly right so relationships have their uses but functions allow us to make more accurate predictions so relationships is a general umbrella we have when it comes to understanding the world around us through functions but when it comes to more precise understanding of the world to be able to make predictions we have functions right functions and functions are a special type of relationship where for given x value there could only be one y value right so this would be a function right because for a given x there's only one y and you can talk about this using the vertical line test that's what people talk about right when you have this type of thing if you do a vertical line you're crossing the function at three different places that's a relationship it's no longer a function so whenever you see a graph right if you see a graph like this or if you see a graph like this all you have to do is do a vertical line test and see how many times you actually cross the function which is basically saying hey for this x value what's your y value right so functions are a special type of relationship where they narrow your choices down to for a given input for a given x value you can only have one output right it's like saying tuna are fish but all fish aren't tuna right this is sort of the hierarchy the the analogy that i use is taking it back to biology where you have your different categories of animals and creatures in the world right there's the i forget what it is i should i usually look this up at the beginning of the year but i forget by the end of the year right but basically you have your kingdom your fauna your your you know we're animals and we're human beings we're animals animals and then we're i don't know what we're categorized as we're categorized in the same group as chimpanzees i guess whatever that is and then from there we go to homo sapiens or something like this it's all subcategories right so each one of these is a branch up here but these guys aren't necessarily just this there's other branches coming off these things right there's other branches coming off these things so there's subcategories so the reason we study functions is for us to be able to understand do predictions in the world right and functions has special type of functions as well there's a whole bunch of functions we've talked about in the past but one of the first ones we talk about are smooth functions smooth functions right and we start talking about smooth functions because they're the easiest ones to understand they have the they're the least complicated and smooth functions are basically any function that's like this right like a lion is a smooth function they can't have points so smooth functions can't be like that they can't have gaps right so that's not a smooth function that's not a smooth function anything with a lion curves and stuff like this they're considered smooth functions and smooth functions we call polynomials right polynomials okay that's what smooth functions are and the first type of function that we look at that are called polynomials are lines right so line is equal to y equals mx plus d and then the next one we look at are parabolas which is y is equal to ax squared plus bx plus c sorry if i'm writing this small but we've talked a lot about this stuff i just want to sort of give you the breakdown of this thing right so a line is like this a polynomial um not a polynomial a quadratic is like this right and then you have other types of polynomial functions the kicker with other types of polynomial functions if you have things like this these polynomial functions tend to be made up of these guys right and we talked about this in an ASMR video we put out regarding our greatest common factor and stuff like this so just imagine taking these functions and saying hey these guys are just made up of these little guys here right a whole bunch of quadratics and lines and whatnot then what we can do is we can take a look at this system if a function represents a system we can take a look at that system and try to figure out what makes things go down what makes things go up and then fine tune that system to if we want to always go up we always go up and if we want to always go down go down or if we want to do fluctuations we do fluctuations right and this goes into investing this goes into athletics like if you're if you're ever doing weight training right um if if you've ever done sports you should go to the gym do weight training but the way it happens with weight training initially you see a lot of results initially your strength goes up your bulkiness goes up your fat content goes down you become healthier basically right initially when you're doing weight training you see great results and then what happens is you plateau out a little bit right and then it's hard to break this plateau and sometimes you actually go down you see your strength go down and then what you see you see another spurt right and sometimes this happens naturally sometimes you actually have to change your diet or change your exercise routine to be able to go to the next step and then you plateau come down go up right and you can do this yourself at the beginning stages by reading and stuff like this but once you go into higher level athletics when it's you know world cup or olympics or whatever it might be there are people who specialize in trying to get you off this plateau and going up again may they be dietitians nutrition coaches or whatnot right so this would be a function and if you can understand what makes people break out of their plateau or specifically you know you have to fine tune it based on who they are and what their body types are and what athletics they're doing this becomes a function and if you can standardize this over different types of people doing different types of athletics depends on the whatever sports they're doing as well right if you can break this down then what you've done you've created functions for different types of sports and different types of body body types to be able to break through plateaus and become better and better and better is this a relationship sure it's a relationship but more specifically it's a function because you can change your input and get one specific output out which is better results just imagine if you you're doing your athletics you hit the plateau and you want to break through this plateau and you change your diet and the diet does good you go up if you change your diet the diet goes down well this now became a relationship you change your diet and you either went up or you went down if you went down then you need to change back again to what you were or something else right so relationship come in handy as well okay sorry if i went off a little bit but this is something that should be as far as i'm concerned a whole chapter should be dedicated to this in early on in high school grade eight or nine try to make people appreciate what these things are that they're studying which they don't unfortunately let me change the view again i hope that answered the question why did we study all the fashions in school poor short poor short chichou as well as is also a character from watch maybe hello there as the as a madius is the the guy who's super smart and super fast who basically set the world to go into chaos in the movie anyway this is mathematical expression of why you need to educate yourself the more variables you can quantify the more accurately you can predict outcomes position or direction this is true in every aspect of life yeah i agree now i kind of understand the more you can understand about the system and talk about the different variables in play then the more you know about that system whatever that system might be smooth functions include much more than polynomials smooth functions include much more than polynomials give me an example race race racer kill like circles are smooth but the relationships they're not functions right let's see i like your beard i wish i was there too touch thanks i do like touching it that's for sure the goatee anyway the beard is i love the beard i miss the beard full beard be respectful please for sure little comments here and there is okay two cases i think so i'm used to dealing with teenagers and teenagers throw darts and throw comments and i think that's the way they like interaction i think one of the reasons for that is because a lot of teenagers and preteen as well they're taken all into groups and put into little rooms and told to be quiet for hours upon hours so when they're able to vent and express themselves they express themselves in whole bunch of different ways it's the nature of the beast it's the way it's it's just the way it is uh yeah for sure thank you for the compliment josh thank you for the compliment josh i do like i do like the goatee i do love the goatee i love facial hair i do love facial hair zany at a party everyone shook hands with everyone else there were 66 handshakes how many people are oh these things always trip me up anybody got an answer for this everybody shook hands how do we go about this problem the definition of a smooth function is a function that is continuous and all its derivatives are continuous so that shouldn't include discrete functions right so exponential functions for example yeah smooth functions so sine and stuff would be two for sure yeah that's right that's right i always just consider that tree and i'm sure but for sure from man i gotta learn my calculus for sine cosine and stuff you can express them as sequences as well or series as well right hey it's all good fun definition of a smooth fun i gotta look into that more i'll look into that more thank you for the correction race racer kill since i deal with mainly high school i gear my terminology specifically for high school to get the ideas across the people so they can understand 12 people is it 12 people that shook hands yeah 66 handshakes how would we go about solving this yeah i'm going to go ahead um how would we go about doing that i'm not strong with my crypto not my crypto with my convictorics and permutations and it's such that n choose 2 equals 66 oh really okay so we would do this let me let me lay it out let me erase this n choose 2 is 66 cool if that's the case then this is the math behind it n choose 2 is 66 so n choose 2 is equal to 66 and this is convictorics right and convictorics there's an amazing documentary out it's called n is the number it's about the guy who was the master of this i think it's called n is the number highly recommend watching that documentary if you want to know the power of this type of mathematics but basically this okay let me write the general formula for this the general formula for this is this n choose r i think r or k they use this is a way uh we express a mathematical formula that allows us to decide how many different ways we can order certain things if we have a certain number that we started with right so n is how many things we're starting with r is how many things we're choosing out of that group of things we're starting with right so the formula for this is it's n factorial over n minus r factorial r factorial and factorial this symbol here we talked about this a little bit right if i write down factorial n factorial what you're doing is we'll do it with a number as well so if i have five factorial here you start off with n and you multiply n by one less than whatever n was so n times n minus one and then you do it again subtract one from here and multiply n minus two etc right now for obvious reasons if this makes sense to you n cannot be a negative number and it cannot be a decimals gotta be a whole number so it could be zero one two three if you know our real number set right we've talked about this real number set okay you got natural numbers whole numbers integers rationals and irrationals right n has to be a whole number which includes natural numbers and it includes zero right so when it comes to n n can't be negative okay and it cannot be a decimal right so if we're going to apply this rule to five this would be five times one less than five which is four times one less than four which is three one less than three which is two one less than two which is one and we stop at one so this goes all the way down to one as soon as you hit one you stop subtracting and multiplying right so five factorial is really five times four is 20 20 times three is 60 60 times two is 120 so five factorial is 120 okay just clarifying what a factorial is okay i'm going to erase this we're going to leave this up so if we're going to apply this formula to this hopefully i'm going down the right path here right yeah i'm going down i'll check the messages afterwards right so what we have here we have the following function if we apply it to this this would be n factorial over n minus two factorial n minus two factorial and r factorial is two factorial now two factorial two factorial is two times one we stop at one so two factorials is just two okay this has to equal 66 so let's expand the n factorial so you see how this works n factorial is n times n minus one times n minus two times n minus three dot dot dot right over n minus two factorial is going to be n minus two times one less than n minus two which is n minus three dot dot dot all the way down to one right we've got one here and we're going to have one here times two factorial and two factorial is just two that has to equal 66 now what ends up happening is because we're just doing straight out division there's no plus and minus between these things each term right you got n minus two and minus three n minus two and minus three these guys killed these guys all the way down right so they're gone so the only thing we have up top is n times n minus one and we've got a two in the bottom okay let me erase here continue this up here so right now we got n times n minus one over two is equal to 66 right so we can cross multiply this up multiply this guy in so this becomes n squared minus n is equal to 66 times two two one twelve hundred and thirty two 132 and then what we can do is bring this over n squared minus n minus 132 is equal to zero so what we're doing now is we're looking for two numbers to multiply to give us negative 132 and add to give us negative one now in this situation the two numbers are one apart because one is positive one is negative because they multiply to give you negative and add to give you negative so the bigger number has to be one more than the smaller number and the smaller number is positive so two numbers are multiplied to give you 132 what are they we could use a quadratic formula let's use the quadratic one should we use a quadratic formula two numbers are multiplied to give you 132 hmm i have to use a calculator to figure that one out let me see oh we got bammers come in solve the handshake thing solve the handshake 12 or 11 12 times 11 oh okay cool thank you for that thank you for doing this so 12 times 11 right that's going to be two one add a zero two one is 132 right so the bigger number has to be negative and the smaller number has to be positive right so this becomes this n minus 12 plus 11 so what you end up having is n is equal to here let me do this in multiple steps and we've talked about the solving quadratics so once you have two things multiplied together give you zero which is one of the powers of zero without this power of zero our mathematics would not be where it is right we would have huge problems right it's the only way to solve this well i'm not the only way but it's the way to solve this once you have two things multiplied together give you zero you can set each one equal to zero so n minus 12 is equal to zero and n plus 11 is equal to zero so n is equal to 12 and n is equal to negative 11 now n is equal to negative 11 according to our definition n cannot be negative right because if we do n factorial you can't go negative 11 times negative 12 times negative 13 you'll never stop you'll never get to one so we kill that answer and the answer is 12 so there are 12 people on the party everybody's shaking hands you would get 66 total handshakes with 12 people shaking hands okay i like the math aspect of it how do how you go about these things with computorics permutations and computorics there's so many different types of problems situations that can come your way that each one requires a certain way of solving things it's beautiful it's beautiful it's just i'm not powerful in taking the work problem and converting it to a solution and permutations or combinations i don't do enough problems like this to be good at it right like hannah said previously use it or lose it right use it or lose it let's see i'm just going to catch up on some of the comments i think the first guy what is the sum of infinity please infinity a progression sequence think the first guy in 12 shakes hands 11 times but you need to subtract one from each person because they've already shook hand with the person before some of all positive numbers there you go infinity did it early bath for that someone like this got timed out thanks for thanks for time to walk you see i don't know what the comments were bedtime okay sweet dreams brother sweet dreams solve this handshake thing 12 or negative yes because n choose 2 is equal to number of two subsets of an n set n can only be positive integers yeah my thinking was because it's like rolling two dice that's where i've got n equals n plus one times n over two oh really i have to think about that in our case he's gone sleep but that's interesting we have to think about it so it's 12 it is 12 yeah negative people seems questionable that could be there could be negative people around who knows right that was fun oh i was solving backwards i did this in a much less mathematical way i just counted the people down by one handshake until i got 66 really how would you do that malik how would you go about or integrating i'm not doing intergirls right now brother i'm not doing calculus my apologies not bad yet by the way i've got to have to go so it's okay casey take off man you gotta take off you gotta take off um it's the what time is it's your eight hours ahead i believe yeah it's friday have a glass brother thanks for popping by 12 11 10 9 oh wow so he did it as a series does that work does that equal 66 what is that three thirty three one two really that's cool what an interesting hypothesis spottings oh that's night ball hey i've got malik message but nightbot stop it nightbot is uh i don't i don't know the sequence starts at 11 i'm not sure why nightbot zap to your thing malik my apologies for that oops nightbot didn't like that yeah i don't know what that was nightbot time by malik for five seconds reason stops running symbols oh symbols hey this is math we're allowed to do symbols i might have to find two nightbots um i know this happened before you should can configure nightbot to not warn people i could try integrating my parts i can't post it because nightbot won't let me you know what let me can you turn up the volume on your mic um i'd rather not mess around with the volume i'll talk a little bit louder let me go to nightbot let me see if i can reconfigure nightbot right now nightbot or should we turn it off we could turn it off uh i haven't been on nightbot for a while um i presume you would change course into another form beforehand i believe so from what i remember in the integration the sign the the trick stuff um they have special functions that you associate them with and stuff doing integration for trick functions is a little tricky is a little tricky from what i remember can you scream you look like you are good at metal screaming i do okay i do okay if you want to know how good i am at metal screaming i put out a little video on what it's like what it's like to be in a mosh pit so basically some of case is posted above but starting at 11 ah okay that's cool i'm gonna head off what's fun but my brains are mushy tonight not been too well last few days oh i hope you feel better brother you too man you too man have some rest drink some nice tea drink some nice tea hey tink how are you doing nightbot timed out is proof oh no okay i gotta kill nightbot how do i okay let me uh nightbot whisper sorry i can't write anything okay i'm gonna how do i kill nightbot i want nightbots commands custom defaults spam protection enable disable access emotes okay i'm disabled cool disabled okay disable disable disable oh no links i'm gonna enable access symbols disabled okay okay guys yes bro there's a nice coincidence between some of first integers and entries too feeling it's bought for us okay reskill and manic uh so i disabled some of the stuff on nightbot hopefully it'll uh you can post what you need to post can i right now try it out try it out if you can do it fantastic i hope so anyway i hope you can do it there's a nice question i don't have the advanced knowledge of mathematical functions to know the language of n choose too so it was great to see it ah cool it's fun stuff that stuff is fantastic and and or two yeah that's basically it what we wrote down here which is oh i think i killed the original one yeah right there if you see this guy right here right is equal to the sum of the first n minus one integers if i send the link to a to a question or arrangements could we have a look at it you know what i've disabled links because as soon as i enabled links people were posting links to phishing sites and stuff like this so links um but what you can do is do on discord i think uh if you go to discord here let me post the discord thing on here cool so there's a discord forum that we have set up if you click on it that should take you to discord except invite and there's a there's a math section that you can post links on so if you post it on there and we're going to come back with another math stream at at 10 30 today right and maybe we're going to take a look at it so if you post links there we can grab the links from there yeah links activate might mean bots come in and post weird links yeah that's the reason i i got nightbot to i linked up nightbot with the live streams was because we're getting some spammers coming in and links being posted i didn't want people to click on links that we're going to go to phishing sites and i want to make sure no one's going to get burnt for this if that's okay colons i'm in the pacific standard on the west coast of Canada so right now we're at 945 am my time okay so i'm basically la time los angeles time in a certain country half of five equals three if the same proportion almost what's the value of a third of 10 um we could do it let's try it out is that even a math question i don't know we could try to lay it out let's try to lay it out so it'd be sort of more of a weighted type of thing i believe join it yeah let me change the view let's see if we can work our way through interesting question used by professional pollsters are one of the reasons why certain viewpoints are disregarded because what they do with them is they give them weighted so this is sort of to me this would be sort of a weighted question right a half of five is a third right so will that even work i don't even know if that works because it would have to be two variables in the weighted problem right because what we're saying is half of x half of five is equal to a third half of five is equal half of five is equal to three half of five is equal to three that's a standard we set so we could do it this way here let's lay it down a half of five is equal to three and the question is this question needs you to invent new math i think i think it does but let's try to invent it why not third of a ten so we want to find out what a third of a ten is right if half of five half of five is a third then a five five is equal to six right and ten is two fives multiplying i mean this is the best i could do with this right so a third ten is equal to two times five is equal to this is what we're looking for right well what we can do is if five is equal to six we'll just substitute six in for five right so this becomes a third times two times six right so one over three is equal to 12 one third times 12 is four so one third of ten is four that would be my answer i don't know if that's legit or not right that makes sense six like a four half a third half of ten a third of ten is that it starts with the premise that five is equal to six yeah so let n equal five yeah so you'll be starting a math stream at gmt from your information gmt time gmt time gmt time is that uh i believe that's uh u k is it not gmt grenish yeah i believe that's u k uh and u k is it should be from what i understand basically we're going to start another math stream in about 40 minutes right we're going to end the stream at 10 my time in about 12 minutes 10 minutes or so and then we're going to take a half an hour break and we're going to do another math stream okay and then tomorrow we're doing four streams and all the times posted for the math streams are my time okay okay so you're back what are you doing back the handshake problem was bothering me i think what my brain was trying to get to was and it was six eyes uh that's solvable or is that time for me to go i think you need to go to bed i think you need to go to bed there there you go it's pst at the moment gst during winter yeah they changed the time i always say pst but i found out they called it pdt now really why it's just weird during winter any cool any cool hikes up in victoria there's lots of amazing walking around in western west coast of british columbia uh in all of canada i've been all over the place in canada i've been to many places in canada i've gone to more places in canada than aside from people i've known in geophysics that have done geophysics excluding anyone that i've met that has done geophysics or geology i've gone to more places in canada than most people i know definitely more more places than my friends and stuff i used to be proud to say i've been to every province and territory in canada that was before they made nunuit nunuit they split up north west territories into north west territories in nunuit so i still have to visit nunuit and there's amazing amazing nature in canada it is raw it is beautiful it's magnificent magnificence yeah so there's lots of amazing hikes up here it's our roots of that question i'm not into integers it's great i'll be back for that cool see you a little later okay awesome brother see you a little later so no solution for integer n um i don't know which question that is so no solutions for integer n i'm not sure if that's the handshake one or if that's the half of five is half of five is what what was half of five is three half of five is three fun um that was a fun math session i like that just random questions right informal because last time we did this we did a whole day with four different streams going on i had some stuff stuff laid out where we did some trigonometry and whatnot i saw spread demographic surfing that last uk general election which major parties were using to target policy so when they were canvassing they predicted that people of certain ages and backgrounds were less likely to vote so their answers had less weight than those more likely to vote if i was doing that canvass i would give more weight to the people less likely to vote because if they came out to vote they found that majority of their their their peers didn't even bother to vote they didn't think it was important these people thought it was that important for them to break away from their peers to vote the the voting methods and the data collected by certain polling stations i've looked at some of that data man some of that data is garbage uh i think you're basically on the right track kasey the right equation is that yeah you're pretty close kasey within the end thing it has to be combatorics you got to do it that way with factorials got you i'm kind of rusty i'll go rest i'm pretty sure about it you should especially if you're recouping really health comes first health comes first i don't know how they make those predictions but it was interesting to note not voting removes policy weight from your entire demographic crazy crazy they should be yeah the voting stuff some people say voting should be mandatory but that makes us gives more power to centralize government for corruption so there's pluses and minuses for everything i just think the best way to to deal with what's going on with our politics is to decouple personal choices with centralized government how we choose to live our lives with a centralized government right they shouldn't be allowed to tell us what we can do on a on a personal basis as long as we're not affecting the community as a whole that we're forcing our opinion on others right which is what a centralized government is doing with their voting and stuff like this right there should be some kind of understanding in in countries and communities of what you know don't harm others and whatnot but what you do to your own body yourself is nobody's business nobody's business in australia yeah that's the that's the one example i know that australia is mandatory but there's a none of the above option that's the option that i want none of the above i would go out and vote every election every minute about none of the above none of the above none of the above unless i really meant to vote for somebody the day before yesterday i was 21 and the next year i will be 24 what day is my birthday the day before yesterday the day before yesterday i was 21 and the next year i will be 24 the day before yesterday so you turn 22 no interesting question i would have to think about that i don't know vote local and if an institution can't effectively enact a policy it should devolve to a level low enough to address it properly i agree i think what should happen with the voting stuff just since we're on it i think all parties anybody that wants to come into power right have the trust of the people you know to get into a certain governmental position right they have to lay down exactly what they plan on doing right and for me 80 percent i mentioned this before 80 percent is legit and if they are able to implement 80 percent of what they said they were going to do then they should be allowed to stay in office if they start reneging on their promises they're gone right it should be a contract it should like it's crazy parties and politicians they promise this moon and the sun and all this jazz to people and then they come to power they do the opposite of what they promise to do they do the bidding of the lobbyists and the corporations and then they're not held accountable to me it just blows my mind if you did that in the contract in some kind of business decision oh i'm gonna do the roofing you know for all your house and you do the roofing for 10 percent of it take all the money and run how is that how is that legit it just crazy it blows me away for me there should be a high levels of devolution and regulation nobody should be unaccountable nobody should be absent i agree i think personally those in power should be held more accountable the crimes that they commit that the general public gets punished for if they're in power and they commit the same crimes and they're they're held you know they're convicted of those crimes their punishments should be in order of magnitude more than the general public because they didn't take on that responsibility to be in charge of everybody else to me the whole concept is weird to me the whole concept is weird okay we're okay we're deviating from mathematics and getting into politics so how about we call it there we'll be back in about half an hour to do another live stream okay government in the west are deceptively weak at the moment small groups of unaccountable private individuals answerable to nobody have all the power i think the governments in the west are extremely powerful i just think they're not held accountable i think they have way too much power way too much power and i could give you examples example after example like it's crazy like even my family has been influenced by it right it's crazy it's crazy but we could talk about that another day thanks for popping in reskill have a good one you guys too you guys too and i'll be back in about half an hour if you want to come back and practicing another mass stream i'm off see you ciao ciao okay gang half an hour break stretch the legs do a little stretch come back with a little mathematics and open discussion again okay see you guys in a bit bye for now