Re: Relative Cardinality

In article <1120590025.089920.6050@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

> Timothy Little wrote:
>
>
> > If there is a bijection between two sets, then their WMCards are
> > "equal".
>
> 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



> Something not
> completely existing can be less than but cannot be equal to some other
> existing or not existing object.

The only something not completely existing here is WM's sanity.
>
> > However, equal WMCards does not mean that a bijection
> > exists.
>
> For finite sets equal Cards (+/- 1) means that a bijection (+/- 1) can
> be established.

If equal WMCards do not imply bijectability even for finite sets, they
are no bloody use for finite sets. We already knew that they are of no
bloody use for infinite ones.

For infinite sets we cannot draw a conclusion about
> equal Cards. Infinity obeys some other rules than just common sense!
>
> Regards, WM
.

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