Re: Relative Cardinality



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

> However, equal WMCards does not mean that a bijection
> exists.

For finite sets equal Cards (+/- 1) means that a bijection (+/- 1) can
be established. 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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