Trying to learn how to write proofs. I decided to practice a direct proof approach.
axiom 1: n is even if n=2k for some integer k
axiom 2: n is odd if n=2k + 1 for some integer k
Theorem: If n is an odd integer, then n^2 is an odd integer.
Let n = 2k+1, for some ineteger k
n^2 = n * n
= (2k+1) * (2k+1)
= 4k^2 + 4k + 1
= 2(2k^2+2k) + 1
This seems a bit incomplete...any feedback?