Simple Proof Methods

A proof is a logical argument that establishes the truth of a theorem using deductive reasoning. Proofs don't need to be too long, technical, or elaborate, but they do need to be clear and unambiguous.

Examples:

Proof. [Sum of even integers] Let $m$ and $n$ be two even integers. According to the definition of even integers, there exists $k_1 \in \mathbb{Z}$ such that $m = 2k_1$ and $k_2 \in \mathbb{Z}$ such that $n = 2k_2$.
Notice that $$m + n = 2k_1 + 2k_2 = 2(k_1 + k_2),$$which is, by definition, an even integer because $(k_1 + k_2)$ is an integer.◼

In $\LaTeX$, proofs are written inside the

proof

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