Proofs

A proof is an argument used to show that something is either unambiguously true or unambiguously false.

Choosing a Proof Method

There is no clear answer to the question of which proof method should be chosen.

$$\begin{array}{c|c} \text{Claim Type}&\text{Possible Method}\\ \hline\\ \text{If/Then}&\text{Direct Proof}\\ \text{Modular Arithmetic}&\text{Cases}\\ \text{Something Exists}&\text{Construction}\\ \text{Sequences/Recursion}&\text{Induction}\\ \text{Stuck?}&\text{Try Contradiction}\\ \text{Still Stuck?}&\text{Maybe it's false, try disprove}\\ \end{array}$$