Re: The definition of finite set

On Sat, 8 Mar 2008 19:43:52 -0800 (PST), Zaljohar@xxxxxxxxx wrote:


Define:

x is finite iff [ card(x) = 0 or
(exists y (y << card(x)) and
for all y ((y < card(x) and y neq 0) implies exists z( z << y)))]

Since you actually DON'T KNOW if your definition is equivalent to the
usual definitions of /finite/, you should define, say,

x is z-finite :<-> ...


Now the question is the following: Is this definition equivalent to
Dedekind definition of 'finite set'?

See? So the QUESTION is:

x is z-finite <-> x is Dedekind-finite ?

(for any x).


IF not, then to which of the definitions of 'finite set' it is
equivalent?

EITHER z-finite is equivalent to ALL definitions of /finiteness/ or with
NONE (in the context of ZFC, of course).

Now it's YOUR TURN to show that z-finite is equivalent to any of the
usual definitions of /finiteness/ in, say, ZFC. After all it's YOUR
proposal.


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