Theory Graph Example

Definition · Even#

$n \in \mathbb{Z}$ is even if $n = 2j$ for some $j \in \mathbb{Z}$.

Definition · Odd#

$n \in \mathbb{Z}$ is odd if $n = 2k + 1$ for some $k \in \mathbb{Z}$.

Theorem · Even plus odd#

If $m$ is even and $n$ is odd, then $m + n$ is odd.

Proof · Add the forms#

$m + n = 2j + (2k + 1) = 2(j + k) + 1$.