Re: The set of necessary FISONs

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

Am 18.02.2025 um 16:32 schrieb joes:

Am Tue, 18 Feb 2025 16:15:47 +0100 schrieb WM:

On 18.02.2025 11:08, joes wrote:

Am Tue, 18 Feb 2025 10:02:53 +0100 schrieb WM:

On 17.02.2025 21:36, joes wrote:

Am Mon, 17 Feb 2025 20:40:47 +0100 schrieb WM:

On 16.02.2025 21:56, Jim Burns wrote:

On 2/16/2025 6:18 AM, WM wrote:

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.

If. Induction doesn’t prove that.

But it is obviously true.

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.

Induction, as applied by Zermelo and others, proves: If every
element is created or described by induction, then the set of all
elements is created or described by induction.

No.

Here in sci.math we should adhere to mathematics.

Indeed.

Then read what they said.

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}.

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

Makes no sense. There is nothing to subtract the set from.

For every set M that doesn’t contain itself, M \ {M} = M.

Such as for the set of all FISONs.

If every element of a set is countable, then the set is a countable
set.

What the fuck, absolutely not.
„If every natural is finite, then there are only finitely many
naturals.”?

Word on this?

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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.