Re: A new definition for Cardinality

Virgil wrote:
In ZF and ZFC every "class" is set, but it is not clear that the "set
of all sets bijectable to a given set" exists at all.

I think you might have meant that every set is a class but that no set
is a proper class.

In ZF and ZFC every object is a set (under an appropriate definition of
a set). But, as you know, in ZF and ZFC, no object is a proper class.

And, if I'm not mistaken, we prove that the set of all sets bijectable
to a given set is not a set. Let B be such a purported set. It's easy
to prove that Ax x in UB, a contradiction.

MoeBlee

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