# Chapter 2: Proof Techniques

The word “proof” is thrown out in all fields, from science to mathematics, all the way to philosophy. In every field, a proof boils down to some information which asserts the validity of a statement. What that statement might be could be anything from any field, but what actually constitutes a proof for that statement differs from subject to subject.

Let’s formally define what a proof is.

## Definition:

ProofA mathematical proof is a

finitesequence of valid steps which, when combined in a specific order, indicate the truth of a specific statement.

The power of a mathematical proof comes in the subtly of a finite proof proving a statement in infinitely many cases. Using proof techniques, a very short sequence of steps can prove a statement for a set as large as the real numbers.