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