Proving that an initial infinite ordinal is a limit ordinal

Question

As in the title,

An initial infinite ordinal is a limit ordinal.

How can I start proving that?

Start by writing down what "initial" and "limit" mean. – Chris Eagle Jan 07 '13 at 00:21 — Chris Eagle, Jan 07 '13 at 00:21

score 3 · Accepted Answer · answered Jan 07 '13 at 00:23

3

Hint: Show that there is a bijection between $\alpha$ and $\alpha+1$ for infinite ordinals $\alpha$.

Consider the case between $\omega$ and $\omega+1$, and see that it transfers to the other cases easily.

answered Jan 07 '13 at 00:23

Asaf Karagila

1 Answers1