Re: a question

On Sep 10, 5:13 am, Zaljo...@xxxxxxxxx wrote:

What is the proof of the following theorem in Z:

Forall x ( (0 in x and Forall y (y in x -> yUnion{y} in x)) ->

 Forall z (z is a finite ordinal -> z in x) )

It depends on the route of theorems and definitions we take. My own is
first to prove that no limit ordinal is finite. Then, toward a
contradiction, let z be the least finite ordinal not in x. So z is not
0 (since 0 in x) and z is not a limit ordinal (since no limit ordinal
is finite), so z is a successor ordinal. But then z=k+ for some finite
ordinal k in x, so z in x, which is a contradiction.

MoeBlee


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