Simple Proof Methods

Before diving into proofs, let's first define some key terms in this area of math:

A definition provides a precise meaning or notation for a mathematical concept. It establishes the criteria that an object (e.g., a number) must satisfy to belong to a certain category. We can state or establish definitions; we don't prove them.

Examples:

Definition. [Even integers] An integer $n$ is called even if there exists an integer $k$ such that $n = 2k$.

Definition. [Odd integers] An integer $n$ is called odd if there exists an integer $k$ such that $n = 2k + 1$.

In $\LaTeX$, definitions are written inside the

definition

environment; see slide 36 for the full $\LaTeX$ code.