/sci/ - Science & Math

>>11616542
>(13) I dont think i was thinking about prime numbers, but that makes more sense
Primes are used for arguments like these because of the uniqueness of the factors. For example, if you want to show that [math]\mathbb{N}^n[/math] is countable for any [math]n\in \mathbb{N}[/math], it suffices to find an injection. In order to construct one, grab any n distinct primes [math]p_i[/math] and define a function [math](k_1, \dots, k_n) \mapsto p_1^{k_1}\cdots p_n^{k_n}[/math].

I think you could probably move forward and read the next chapter. If some claim seems odd, then you can return to the mapping chapter, as (if I remember correctly) the first example of a group he gives you will be automorphisms, and the claims he makes will be about bijections (or can be verified more concretely using those), like for example associativity. Keep up the good work, anon!