User blog comment:Edwin Shade/Defining LOCC (Language Of Ordinal Construction)/@comment-32697988-20170924234138/@comment-32876686-20170925003203

Ordinal tetration is defined using the '^^' symbol, ordinal pentation and successive hyper-operators can be formed by creating recursive equations that describe successive tetration, and so on.

The ordinal $$\omega^^{\omega}2$$ can be defined as $$\omega$$:{b$$\mapsto$$b+1},$$\omega \uparrow \uparrow (\omega*2)$$.

In order to use an ordinal, we have to define it first, once we do we can use the name of the ordinal, (which is to be denoted by one arbitrary symbol of preference), and define higher ordinals in less space.

The following gives an example of this, where omega, (here represented by an a), is defined once so it can be shown twice without having to write out it's explicit definition twice.

The ordinal $$\omega ^^\omega ^^\epsilon_0$$ can be defined as a^^a^^b,a:{c$$/mapsto$$c+1},b:{d$$\mapsto$$a^d}

Note that in both examples I said "can be defined as", because there are much more ways to define the same ordinal, but I just choose what first came to mind.