Re: Relative Cardinality

In article <1120676745.100319.258130@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

> Virgil wrote:
>
> > > Unjustified conclusion. If there is a bijection possible between two
> > > well-ordered sets A and B, then we find that Card(A) =< Card(B) and
> > > Card(B) =< Card(A). For infinite sets Card(A) = Card(B) cannot be
> > > concluded, because they do not actually exist.
> >
> > Then WMCard does not measure set sizes.
> >
> > Set sizes must satisfy: If a <= b and b <= a then a = b
> >
> That is a fairly primitive rule extrapolated from finite sets.

What other "primitive" rules of ordering is WM's silly relative
cardinality to be exempt from? Until WM can provide a list of those
order, and other, properties which hold and those which do not, his
definition is without provenance.


> Potentially infinite sets

Sets never exist in WM's real world so it does not matter in the least
what WM claims about their behavior in that world. Sets only exist in
the world of ideals in which WM's strictures are of no effect.

In the ideal world, where all sets live, there is no such distinction
between potential and actaul as WM posits for his matereial world.
.

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