Finite : A definition

Hi all,

The following is my definition of 'x is finite' and I think it is
equivalent to the standard definition:


x is finite <-> E!y (y is a V.N. ordinal & Ef(f:y->x,f is bijective))

V.N. stands for Von Neumann ordinal.

In words: x is finite if and only if there exist a unique Von Neumann
ordinal that is bijective to x.

One can see that all Dedekindian infinite classes are bijective to
multiple V.N. ordinals.On the other hand a 'Dedekindian finite that is
at the same time a standard infinite class' will not have a bijection
to a Von Neumann ordinal.

So the above definition is equivalent to the standard definition.

Zuhair
.

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