Cantor's Absolute Infinity

Cantor's Absolute Infinity was an infinity proposed by Cantor that made up the collection of all ordinals. Due to the requirement of ordinals to be well-ordered, this is not itself an ordinal.

It is commonly denoted with the symbol $\Omega$.

Proof $\Omega$ is not an Ordinal

Suppose $\Omega$ is an ordinal. Then $\Omega$ has an ordinal successor $\Omega ^{+}$ and $\Omega \in \Omega ^{+}$. But $\Omega ^{+}$ is an ordinal, so $\Omega ^{+}\in \Omega$. Since ordinals are well-ordered by $\in$, $\Omega ^{+}\in \Omega ^{+}$, but this violates the requirement for a well-ordering to be well-founded, so, by contradiction, $\Omega$ is not an ordinal.

Other uses

Voidsecond - Is the time equivalent to the reciprocal of Cantor's Absolute Infinity. Too short to be useful in any practical cases