/sci/ - Science & Math

>>9407745
and you can add an infinite number of rational numbers together and get an irrational at the end. All of the partial sums are rational since the rationals are closed under addition but putting infinity in makes everything go to shit.

so what I'm saying is your post is wrong

w-w-what's a fourier transform? is it a function that takes in functions and spits out a sequence of frequencies?

>the min(set) is the smallest element of that set
>min(N) is 1
>all subsets of N have smallest elements

>the gcd of two natural numbers m and n is the smallest elements of S c N: k=mx+ny, x,y being elements of z --- this is never empty as long as m and n are not both 0

>e.g. let m=4,n=8. then k=4x+8y=4(x+2y), with x=-1,y=1, we get k=4(1), and as 1 is the smallest element of N, it must hold that k=4 is min(S) as S is a subset of N

is this valid or am i missing something here?

are peano axioms covered in bourbaki books?

Why are addition and multiplication commutative?

Every math book i read starts off talking about how it assumed this. Why isn't there a proof of some kind?

isn't this a big flaw in math? you say you make a proof of all these things like the fundamental theorem of calculus and the fundamental theorem of algebra, yet you can't prove what you used to prove them with.

instead it's "let _____be commutative/associative/distributive under this set"; why can't we prove this first?

am i being insane? it seems off that math touts rigor then does this.