User:Ubersketch/Guide to Googology/Cantor Normal Form

The mathematician Georg Cantor created a way to represent ordinals up to \(\varepsilon_0\). Today we will be discussing this system.

Every limit ordinal up to \(\varepsilon_0\) can be represented like so:

\(\omega^{\alpha_0}n_0+...+\omega^{\alpha_k}n_k\) where \(\alpha_x\) is an ordinal in Cantor normal form and \(\n_x\) is an ordinal in Cantor normal form.