Getting Started

I'm starting this blog to publish some thoughts, theorems, and proofs of those theorems. I see myself in the near future writing on the topic of prime numbers of the form 6n ± 1. Here is an example of a proof of a theorem on the topic.

[Note: I think my friend Avery Cotton is at slight confusion over the definitions of proof of contrapositive, and proof by contradiction. It is my understanding that proof by contradiction is a proof strategy in which one assumes both the negation of the conclusion, and the hypothesis (example: to prove "if P, then Q" by contradiction assume P and assume not Q). This works because the contrapositive (if not Q, then not P) is logically equivalent to the argument (if P, then Q). Therefore assume the the hypothesis and the negation of the conclusion and you will arrive at a contradiction if and only if the argument is valid.]


The strategy "proof by contradiction" examines the highlighted portion of the truth table. By showing this you show the argument is valid.