Re: The reality of sets, on a scale of 1 to 10 [Was: The non-existence of "dark numbers"]

Am Sat, 22 Mar 2025 09:47:22 +0100 schrieb WM:

On 21.03.2025 20:37, Moebius wrote:

Am 21.03.2025 um 19:48 schrieb Alan Mackenzie:

WM <wolfgang.mueckenheim@tha.de> wrote:

 

Learn that [...] Cantor [once] has [uttered] that the positive
numbers have more reality than the even positive numbers. He said
that is not in conflict with the identical cardinality of both sets.
And he was right!

I doubt very much Cantor said such rubbish.

Actually, WM is right here. But the notion of "more reality" clearly
wasn't meant as a technical term (by Cantor). He -Cantor- was just
trying to explain the mathematical fact that 2IN is a PROPER subset of
IN, while both sets still have the same cardinality.

Yeah, one can just talk about subsets, and nobody disputes that.

This proves that cardinality does not concern quantities but only judges
the behaviour of potentially infinite sets: They go on and on. Every
pair of a bijection has infinitely may successors. A final
quantification is impossible.

No, there are also finite cardinalities, and "actually infinite" sets
like N also have a cardinality (all infinite sets go "on and on").
A bijection doesn't have to be ordered. What do you mean by
"quantification"?

(I'd dare to bet that this was the only time he ever used that phrase
in this context.)

You would win.

Then you shouldn't abuse "reality" like that.

Hint: WM is all about words.

Reality is more than words.

*facepalm*

--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.