User blog:Edwin Shade/Enumerating the Countable Ordinals

A Scheme For Ordinals $$<\epsilon_0$$
Just seven symbols are sufficient to intuitively represent all ordinals less than epsilon-nought. PEMDAS is used when evaluating expression, such that parenthesis need not be used in every single case.

$$0\cong\text{0}$$

$$+\cong\text{1}$$

$$\cdot\cong\text{2}$$

$$^\cong\text{3}$$

$$\omega\cong\text{4}$$

$$(\cong\text{5}$$

$$)\cong\text{6}$$

For example, $$\omega^{\omega+3}+2\cong\omega\text{^}(\omega+\omega\text{^}0+\omega\text{^}0+\omega\text{^}0)+\omega\text{^}0+\omega\text{^}0$$

$$\cong\text{435411430143014306114301430}$$

'This is a work in progress, and I will eventually include ennumeration schemes for all ''countable ordinals. To those who are thinking this is impossible as the set of countable ordinals is uncountable, I assure you I am aware of this, and have already devised a solution to this.'''