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# Rgetar

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• ## Ordinals array function

June 6, 2017 by Rgetar

I interested in ordinals, and I asked myself: "Why we use $$\omega$$,  $$\omega2$$, $$\omega^2$$, $$\omega^\omega$$, $$\epsilon_0$$, $$\zeta_0$$, $$\phi(3,0)$$, $$\Gamma_0$$ etc. instead of $$\omega\uparrow\uparrow\uparrow\omega$$, $$\omega\uparrow\uparrow\uparrow\uparrow\omega$$ etc.?"

But I realized this doesn't work beyond $$\epsilon_0$$ since $$\omega\uparrow\uparrow(\omega+1) = \omega^{\omega\uparrow\uparrow\omega} = \omega^{\epsilon_0} = \epsilon_0 = \omega\uparrow\uparrow\omega$$.

I experimented and created a BEAF-like system, suitable also for ordinals.

It is family of functions [X]a of ordinal a.

Let X - sequence of ordinals (or "negative ordinals", i.e. ordinals with "-" sign before them) with separators.

All zeros we may omit.

All lef…