Re: abundance of irrationals!)


Randy Poe wrote:


> If the set size were finite, you would reach a point where
> there is no next.

If the magnitude were finite, you would reach that maximum.

If by definition the magnitude is always finite, and that works, why
can't, by definition, also the cardinality be always finite?
>
> Do you think there exists a finite integer n such that n+1
> is not an integer, or is not finite?

Do you think there exists a finite number of elements such that adding
another one the result gives an infinite set?

Remember: Every set of even numbers contains numbers which are larger
tan the cardinality of that set. This is valid for *every* set of
finite numbers. There is no reasonable arguing claiming that this
situation should change in case of an "infinite" set. Also some
elements of an infinite set of even numbers would necessarily surpass
the cardinality.

Regards, WM

.

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