Re: Simple enough for every reader?

Am Mon, 16 Jun 2025 12:50:58 +0200 schrieb WM:

On 16.06.2025 09:41, Mikko wrote:

On 2025-06-15 16:15:39 +0000, WM said:

On 15.06.2025 12:32, Mikko wrote:

On 2025-06-14 14:00:36 +0000, WM said:

The complete set of prime numbers is infinite.

(There are also infinite subsets of the primes...)

Mathematics is restricted to mathematical things even when the
inspiration comes from something non-mathematical, as it often comes.
Things that depend on time or otherwise on the real world are not
mathematical.

That is a wrong opinion, as best can be seen by geometry. But also the
restrictions of reality do limit what can be expressed in mathematics.

Geometry doesn't depend on time; perfect lines do not exist. Does
mathematics shrink like the observable universe does?

But that is not the usual approach. The undefinable prime numbers for
instance belong to present mathematics.

Definability is a mathematical property. Every natural number and in
particular every prime number is definable.

Then define the prime numbers such that none remains undefined. Or
define a hitherto undefined prime number.

We're working on it. Do you think the largest known prime is undefined
or undefinable?

Then can as they do. The arithmetic order of natural numbers is a
known well-order. But a well-order does not imply that there is a
last one. only that there is a first one.

But this does: ℕ \ {1, 2, 3, ...} = { }    .

No, it does not. There is no last one in { }.

When the natural numbers are subtracted one by one and when finally none
remains, then a last one has been subtracted. This is forced by their
order.

No, order does not force finity. Infinite sets can be well-ordered.

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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.