Re: The set of necessary FISONs

Am Fri, 21 Feb 2025 18:17:32 +0100 schrieb WM:

On 21.02.2025 11:37, joes wrote:

Am Fri, 21 Feb 2025 10:39:46 +0100 schrieb WM:

On 21.02.2025 02:18, Richard Damon wrote:
>

In order to secure the existance of "infinite" sets, we still need
the following axioms.

Almost correct, but only singular: we still need the following axiom.

>
There is no mention of "induction" in the statement.

The following axiom is the axiom of induction. The set Z contains the
empty set as an element and with every element a also the element {a}.

Yet not the element Z.

Zermelo claims to secure the existence of set Z.
This set can be handled, for instance removed from Z. A set containing Z
is not useful in this context.

Z is not a set containing Z; Z cannot be "removed" from Z.

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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.