Re: Relative Cardinality



Virgil wrote:

> > Recently we had a proof that sqrt(2) is not rational. We should
> > concentrate on more general problems: It is impossible to label more
> > than 10^100 entities by all particles the univese supplies. Therefore
> > there cannot exist a set with more than 10^100 elements and we cannot
> > count up to 10^10^100.
>
> What happens in the physical world does not govern what happens in an
> axiom system. Such systems are not subject to any physical limitations
> but only the limitations of what the axioms themselves state and the
> imaginations of those who investgate them.

Two elements of a set must differ by at least one property. That is
required by set theory. This property may be such a tiny thing as the
spin of one electron or a huge amount of billions of billions of
electrons and protons and neutrons building those neurons of your brain
which are required if you bother to realize this difference as an
"idea".

Regards, WM

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