30 Aug, 2025 Here's how mathematical proofs generally work. You start with some statement. Say, something like: Let G be a finite group. For all x∈G, there is some positive number k≤|G| such that xk=1. A standard mathematical proof is then a list of statements with the last one following from the previous ones: If G is a finite group, then consider the set S={1,x,…,x|G|}. Note that this set S is contained in the set of elements of G, which has size |G| Since there are |G|+1 powers of x in S, the...