Re: The set of necessary FISONs

Am Thu, 20 Feb 2025 11:26:13 +0100 schrieb WM:

Am Wed, 19 Feb 2025 17:16:15 +0000 schrieb joes:

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.

Will the human race go extinct if we don’t achieve immortality?

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.

Sure. Nobody is arguing against that.

Fine. Induction covers all elements of an infinite inductive set. There
is no k+1 remaining.
Subtraction of all elements leaves the empty set.
UF = ℕ ==> Ø = ℕ.

Substitute: UF = X != N. Does it follow that X = {}?

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.”?

The set of all natural numbers which can be defined is
finite. infinitesimally smaller than ℕ.

Is that because every natural is finite?

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.