Fax Uncountable Us State with airSlate SignNow

Line up numbers log

hey Vsauce Michael here what is the biggest number you can think of a Google a googolplex a milli million all Plex well in reality the biggest number is 40 covering more than 12,000 square meters of Earth this 40 made out of strategically planted trees in Russia is larger than the battalion markers on Signal Hill in Calgary the six found on the above and badges in England even the mile of pie Brady unrolled on numberphile 40 is the biggest number on earth in terms of surface area but in terms of amount of things which is normally what we mean by a number view big 40 probably isn't the biggest for example there's 41 now and then there's 42 and 43 a billion a trillion you know no matter how big of a number you can think of you could always go higher so there is no biggest last number except infinity infinity is not a number instead it's a kind of number you need infinite numbers to talk about and compare amounts that are unending but some unending amounts some infinities are literally bigger than others let's visit some of them and count past them first things first when a number refers to how many things there are it is called a cardinal number for example for bananas twelve flags twenty dots twenty is the cardinality of this set of dots now two sets have the same cardinality when they contain the same number of things we can demonstrate this equality by pairing each member of one set one-to-one with each member of the other same cardinality pretty simple we use the natural numbers that is 0 1 2 3 4 5 and so on as Cardinals whenever we talk about how many things there are but how many natural numbers are there it can't be some number in the naturals because there'd always be one plus that number after it instead there's a unique named for this amount aleph-null Aleph is the first letter of the Hebrew alphabet and Aleph null is the first smallest infinity it's how many natural numbers there are it's also how many even numbers there are how many odd numbers there are it's also how many rational numbers that is fractions there are that may sound surprising since fractions appear more numerous on the number line but as Cantor showed there's a way to arrange every single possible rational such that the naturals can be put into a one-to-one correspondence with they have the same Cardinale point is aleph-null is a big amount bigger than any finite amount a googol a googolplex a googolplex factorial ^ a googolplex - a googolplex squared times Graham's number Aleph Nolan is bigger but we can count past it now well let's use our old friend the super task if we draw a bunch of lines and make each next line a fraction of the size and a fraction of the distance from each...