Cc Uncountable Formula with airSlate SignNow

Send uncountable number

so a very natural question to ask I'm so glad so an Austin natural maybe a real christian ask anyway is is well if you can play this game VR and say that these two sets are equal in size can you always do this hmm so here's what we going to do I am going to try and play the same game with the real numbers and then show you why it doesn't work okay so um quicker is you know what what makes a real number different through a rational number what kinds of numbers are real but they're not rational yeah oh you're thinking of you're thinking of the difference between real and like complex okay big things simpler we know what rational numbers are what does it mean when I was not rational we know that these numbers are right here's an example okay 1 1 & 2 oh look it's not a ratio between any two integers it's its own theme okay now this is very important you actually um I'm actually gonna get so month audience-participation here I think there are 12 digits when you're calculating your space so I looked at first of all people who have calculators to get them out and stand at the front okay so if you get a calculator so I've got one here's a whole bunch of real numbers okay and by the way just for the record yes you could totally just make up numbers as you go okay but the point is what were you trying to do is write down well we can't write that all of them but just imagine that we could write so you know dot dot dot and it just keeps on going forever now my game before was to say for look okay here's your real numbers okay I'm just gonna match these all up to what am i doing integers okay I can do that there are problems look they will just go down the line like this so I'll make this matched up with one and two and three and full and so on okay it's your like what's the big deal it looks like I can use the same logic and I can prove that these are the same ah except there's a problem there's a problem and I'm gonna show it to you with another diagonal watch this okay so our assumption was that this list of real numbers if it went on forever has all of the real numbers on it okay but I'm about to prove to you that no matter how long this list Dory's this list can go on forever you still be missing a number watch this I need some space what I'm gonna do is I'm going to form a diagonal here I'm gonna make a new real number right and I'm gonna try and show you why even if this list goes on forever the real number I make up will be different to every single one that you write down and there can be an infinite number of you might end up watch this I'm just going to start with zero point cuz everyone Hofstede turned into peer pressure okay well I'm gonna do so let's just start with this first number here remember what am I trying to do I'm trying to make up a real number that isn't on your list so I'm just gonna say welcome let's look at this first decimal place here okay all I'm gonna do is in my manufactured number I'll just make sure my decimal for this first place is different to that one I'm gonna make it same let's just add one three okay now automatically this I don't I don't care what the rest of it is okay this number is already different to the one that's first on the list so far so good you're like well there's a lot more numbers on this to going it's alright I have infinity on my side only on the second number I look at the next decimal place and I say well I don't wanna match up with that one either I'll just make it different I'll just add one this number no matter what comes after here or here or here will always be different than both of these numbers does that make sense I've already got this comment this point of difference may yell I bought out the phone number well it's cool I'll just make sure the decimal place is also different I'm just adding number one and I'll make sure it's different to this on line one make sure is different to this one that's my last one now have a look with me this number that I just written up the top in green this number is clearly different to every number that you have written on the board and that's that's kind of obvious right because there aren't that many members of it but here's the thing your list which goes on forever right my numbers gonna be different to all of them even though your list goes on forever I've got a number that you missed you remember this is all about matching up things right actually not matching our matching up I found a whole band at all I can find another hole instead of adding one I can just take away one from every digit right that'll be two subsonic one one six one nine zero two six zero five look this number isn't on your lists either right in fact I can come up with an infinite number of numbers that aren't on your infinite list it's a lot of holes so therefore with a different kind of diagonal what I proven is that even though you'll this goes forever like the number of integers that's how many of these you have because it goes on forever right will always be less than the number of real numbers okay now this is really mind-bending right because how are all the numbers this is why I asked you for to put zero point on front of your thing right all of these numbers all these numbers are between zero and one aren't they there are between zero and one and I just said that all of these numbers are more than all of the counting numbers so that means there are more numbers between zero and one then there are from one two three four five forever there are more numbers nestled in that little gap there then there are in the whole list that's weird that's weird now to talk about these two different kinds of infinity it's a bit weird it's like you know infinity is less than infinity that's a bit strange so we need to your language for this right Marc Marquez are here on this Infini over here because it comes from counting one two three four we call this a countable infinity but yes it's an infinity and it goes from but I can count it I can just go on to the right and if I kept forever I'll match up one two one this guy this guy this is way bigger that this is you can't counter the Khan Academy no matter how long we count I'll always come up with more that aren't on your list this is called and uncountable infinite okay so you can say things up sips are countably infinite or unaccountably infinite and that tells you how much bigger one is than the other now the real question to bend your mind is if you call this like this is not a proper notation by the way but you're like well okay countable right is less than all new counts moves me but how much less well how much bigger is is this than this you're like oh you don't think 10 times bigger than two it's five times bigger right how much bigger is this then this is it a counter or infinity or is it an uncountable so anyway there you go yeah what's the point about this right this is all just to put some more meat on the bones of when you say oh yeah you know infinity this infinity that well which infinity do you mean and there are other kinds these are just two of the infinities how many kinds of infinities do you think there are I is there an infinite number infinity is it a countably infinite number of infinite one can you get me so yeah I'm gonna I'm gonna start I'm gonna stop