Algebraic vs. Transcendental Numbers

does this list look familiar these are numbers we know about right we gave them labels what are all these guys up here this one actually should be Kishin it sorry these guys are the counting absorber the natural numbers right okay are these ones these are so they're inclusive of the natural ohms you get the integers right these guys okay I suppose you could say it did - but if I include all of those it's just good okay uh what about these guys were they called they call you rationals right okay how about these guys in here these are actually also in this same camp right they're just little bit different okay what do you call these now you could call them irrational but if you just consider all of these together right remember we did the Venn diagram extended these guys are real and then that leaves us with so I imagine or if I added other numbers you get the comics all right now get this okay all of these numbers together and I think I think we have fire in there somewhere as well with vigor we would fife it is fire natural no is it is it an integer no it's not rational is it it had been here wouldn't it I think fire would be here all of these numbers believe it or not are all actually part of one big family and here's your heading for today all of these numbers are called the algebraic numbers algebraic numbers so this is a bit like if you want to think like ah if you want to think of biology right you know how there's like species and then there's what's above a species a genus which is is there anything above Jesus what about you families okay and you're like it's like me and like you know jellyfish what are we having comments I will wear carbon-based or whatever all of these things they have in common this now why do you think they're called like we get why rational numbers are called rational numbers even to an extent we get why natural numbers are called that why are they called algebraic of Zeppelin okay because all of these numbers that when you were creating your expressions what you are really I didn't tell you this but you were creating equations right all of these algebraic numbers you got they're all solutions I don't know about this one but you know yeah they're all solutions to these equations and these are algebraic equations we use the tools of algebra right and when you solve every one of these you'll get an algebraic number okay now here's the weird funky thing there are numbers that don't belong so this set okay and this is feeding into our next topic of math error and things that what is math is math to discover it that was a big debate point Marla I really loved reading all the disagreement and anger and no you're wrong of the discussions over we have writing their numbers that don't belong here right that these numbers are what we've invented this is what I put to you okay they have been created and formed and found through invented means but there are numbers that aren't in here and I'm going to give you two actually you kind of know what they are the first one is the big that it will absence from here right what's the big superstar number of mathematics it's pi it's part now just consider this with me for a second where do I come from where is it contract ready confer yeah good very close it's about it's about the circumference so the conference versus the diameter right so it's a very simple shape it's very simple shape but you know if you guys know we're into thinking deeply about simple things right so this number this number comes out of this and guess what you can't build it anywhere using algebra it's impossible right if I had to put it this way a PI is not the solution sorry that's an abbreviation Al's transmission to any polynomial equation that's the fancy way of saying right you can write any polynomial your life you guys are seen probably those before you know you got squares you've got plus minus fours whatever you like right there's no pollen you can write where pi will be one of the solutions or one of the one of the roots if you were drawing it back okay now we know what PI is the other one and I sort of mention it very briefly is e okay now if you have your calculator that you can get E and yeah we have talked about this briefly and passing before super I don't want it to here's how we're going to do I'll show you how we get it and then you'll see how it's well maybe you'll be able to work out why it's be okay put your pens down for a second which place down I'm gonna give you a metaphor right and then it'll get us to this number this strange number okay let me take you to a bank take you to the bank okay now if you go to the bank okay and you say well I'm gonna invest some money you're going to get interest back for your money right now I know we talked about simple and compound interest but simple interesting that one really pays signatures so compound interest what is science reading hey what is the compound interest formula here tom it's a times 1 + through that ok now one of the pieces pay for principle the amount of money you're putting that off all right like percentage and for ya number of years months whatever now I'm panicking now so far so good we're still using algebraic tools okay now I hope you see you know the amount that you put in there doesn't matter all that much it's not that important for you you can put in $1,000 $5,000 I'm just going to imagine what if you just put in $1 okay the reason why is I don't know if you want it was due a bit of an experiment okay suppose you have $5,000 what do you think is better putting it in one bank account with $5,000 or putting it in 5,000 Vanya's each with a dollar in them which one is better no it's kind of funny assuming they have the same think of the fees MSU means no fees same interest rate actually there's no difference oh you can go ahead and prove it for yourself if you like we can use this boy southern hark about but for that reason I'm just going to consider a dollar because then if you have more than a dollar it's no big deal alright now let's suppose is a really generous place really really really generous okay and it gives you an interest rate of 100 percent okay so you know this bag is this bag is run by someone with very very deep pockets like you know saying see me okay obviously my friend wouldn't be Rubbermaid but suppose now here's the thing right um if we put it in for say a year right then that'll be you know one but actually you guys know it actually doesn't wait there sit there for a whole year and then double right in fact our banks they give you interest a little more frequent in that how often they'll they'll pay you every month but they actually calculate it every single day did you know that now if you if you've got a baby you can go and log on and you can see it's like oh cool I earned 3.2 cents today something trivial like that but happens now being that each day you're actually getting one little fraction of the interest this number changes doesn't it right it's not much change it it's going to be the contacts which is 365 okay so therefore I'm Katherine how much will you have at the end of the year no seriously how much we have don't work out you got a calculator this 100% right it's just one they're like whoa whoa what did you get to a point now hold on a second you're like huh that's a bit that's a bit funny but wait a second if you know I didn't do it frequently if I didn't do every day you just at the end of the you just get doubled right if you doing every day you get more what if you did it more frequently what if you didn't say say there's 24 hours in the day right so every hour let's do it every hour right which means that this is going to be sung as before right so you wouldn't get two point seven one four five six seven anymore will you what do you get you get more right but how much what do you get what do you get come on give me some decimal places on yeah this eight one two yeah like no more come on how about not every hour how about every minute what do you get what do you get I can tell you now you're probably gonna get to eight something something like that okay in fact what you're going to get is this something okay now what have we just done what we are modeling right now is something that grows and as it gets bigger right it grows faster don't make sense because you know the more money that's in there the more interesting to those that's the way compound interest works if I drew it it would look like this starting off at $1 yeah it's an e for exponential curve like this number this number this is the number of exponential growth everywhere in the universe and you can't build it like this we sort of DIN right but what you really into it like these things won't give you this exact number right you have to keep on doing if you keep on doing it forever okay so these two guys they're the big important numbers in math now ready for me this is just a side note just a little thing turn funky out of them better these numbers they're not just randomly connected and cool right if you take 80 unfortunately your calculators countries unless you have a pic if you have an F X 100 you might but if you raise it to the power of Pi you'd expect that to be a weird number right oh if you raise it to the power of I times pi get that yeah you probably don't have my calculator I mean what you know it'll spit you back in math era it won't do it so what's this about he's a weird numbers so in summary you know all these other here these are what we call the algebraic numbers the numbers we can build without turning these numbers over here they come from they come from somewhere else we didn't make these things we didn't design this is everywhere in the universe it sort of it transcends the tools that we have for building numbers which is why they're called transcendental numbers let me say that again you got all these numbers over here this huge family of numbers that we can build through algebra and then you've got these reared guys who they are real obviously we're not not this kind of real are there there's some kind of number but they transcend the tools that we have for building on this the transcendental numbers okay now they're not the only ones in pi but they're the most famous ones

Channel: Eddie Woo

Views: 51,540

Rating: 4.9170732 out of 5

Keywords: math, maths, mathematics, Algebraic Number, Transcendental Number

Id: X5TU1Hyi-S4

Length: 13min 30sec (810 seconds)

Published: Tue Sep 09 2014