Re: Simple enough for every reader?

Am Wed, 02 Jul 2025 15:51:01 +0200 schrieb WM:

On 02.07.2025 09:45, Mikko wrote:

On 2025-06-30 18:21:09 +0000, WM said:

On 29.06.2025 12:25, Mikko wrote:

It means that no further element can be found later on.

Whether an element is "found" has no mathematical meaning and in
particular does not affect its being or not a member of some set.

"Numerals constitute a potential infinity. Given any numeral, we can
construct a new numeral by prefixing it with S." [E. Nelson: "Hilbert's
mistake" (2007) p. 3]

Yeah, nothing about "finding" in there.

Then it cannot be. If it is that all natural numbers are subtracted in
their order, then it is that a last one is subtracted.

Given two sets there is a set that is their difference. There is no
opeartion of subtraction in order.

The set ℕ has an intrinsic order which can be used at any time.
Bijecting sets presupposes and requires order. Further the difference of
sets depends strongly on the order assumed.

Bijections don't require order. Set difference has no order.

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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.