Re: An uncountable countable set


Tony Orlow schrieb:

Hi WM. I agree entirely with your analysis regarding the interdependence
of the existence of the infinite set of naturals and the existence of
naturals of infinite value. This leads to the conclusion that the set of
finite naturals is finite, though unbounded, since as you say, there
cannot be an infinite number of differences of 1 where no two elements
are infinitely different. In order for an infinite difference to occur
between two natural, one must have an infinite value.

Hi TO. This opinion is easily proved by Franziska's recognition that
there are omega differences. It is simple to see that omega*1 = omega.

However, I wonder whether you would ever consider the existence of
infinite natural numbers.

Then these numbers would not deserve the name "natural number".

After all, your argument says that either you
have a finite set OR you have infinite values in the set. Is the second
option objectionable for you?

What would infinite values be good for? Distinguishable infinite values
are provably inconsistent (see my binary tree) and to have one infinity
the approved potential infinity is sufficient.

Regards, WM

.

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