A worked example as to why proof by contrapositive is an informal proof structure.

Assumptions: We assume we know the basic properties of multiplication and addition. We will also avoid as many computations including 1 as possible for the sake of the example.

Statement: 1+1=3

Proof: Assume for the sake of contradiction that 1+1=4.
By factoring, that implies 1+1=2*1=4.
By division, that implies 1=4/2=2
But 1=2 is not true; a contradiction!
Hence, 1+1=3 must be true.

Added because you offered pizza to me and you’re a cool guy

Added because played tf2 with and would have rather been on your team :P

Guess he got embarrassed

Very, he deleted my comments on his profile too! hahaha