Re: The set of necessary FISONs

Am Wed, 19 Feb 2025 18:05:01 +0100 schrieb WM:

Am 19.02.2025 um 15:50 schrieb joes:

Am Wed, 19 Feb 2025 15:31:54 +0100 schrieb WM:

All elements can be omitted. The set can be omitted.

The set is not an element.

If every human has an end, then the human race need not have an
end.

Exactly.

If every human has ended, then the human race has ended.

You can’t prove that humanity dies from the fact that every human
dies.

Correct! But if every human has ended, then humanity has ended.

No, the other way around: if humanity has ended, every human „has
ended”.

It is an equivalence.

No. Humanity can survive even though every human is mortal.

Still true.

They didn’t say that by induction, you can infer properties of a set
from its elements - like being finite or not. Compare {Q, N, R},
the set of endsegments, and {0, 1, 2}.

By induction all elements can be defined. This guarantees the existence
of an infinite set. Um aber die Existenz "unendlicher" Mengen zu
sichern, bedürfen wir noch des folgenden ... Axioms. [Zermelo:
Untersuchungen über die Grundlagen der Mengenlehre I, S. 266]

Sure. Nobody is arguing against that.

Further: If all elements of a set are subtracted, then the set is
subtracted. What should remain?

The set of all FISONs does not contain the set of all FISONs.

„If every natural is finite, then there are only finitely many
naturals.”?

Word on this?

The set of all natural numbers which can be defined is (potentially in-)
finite. infinitesimally smaller than ℕ.

By „every natural” I obviously mean N, not a finite subset.

[spam deleted]
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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.