Successor of Omega

Theorem

 * $\omega + 1 = \lbrace \N, 0, 1, 2, ...\rbrace$

where $\omega$ represents the smallest infinite ordinal and $\omega + 1$ is the successor of $\omega$.

Comment
It is customary to use $\omega + 1$ rather than $\omega^+$ for transfinite arithmetic. However, keep in mind that this isn't "regular" addition.

For example, $\omega + 1 \ne 1 + \omega$.