Re: Relative Cardinality



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.
Potentially infinite sets are never complete and, therefore, have no
sizes which could obey that rule.
My tool can only show that a set is not surpassing another by
magnitude. Equality is nonsense with infinite sets.

>
> > 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.

Do you really need that kind of arguing? - already at this stage?
> >
> > > 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.

They are of excellent use to determine the truth! I notice your
reaction!

Regards, WM

.