Re: The set of necessary FISONs

On 06.02.2025 03:29, Richard Damon wrote:

On 2/5/25 12:32 PM, WM wrote:

On 05.02.2025 18:19, Jim Burns wrote:

On 2/5/2025 4:14 AM, WM wrote:

>

Either way, the axioms do not create,
but only describe.

>
The axioms of non-standard analysis or string theory create.
But that is irrelevant for our topic. The axioms of Peano, Dedekind, Cantor, Zermelo, Schmidt, v. Neumann, Lorenzen concern all natural numbers with no exception by induction. By the same induction I can remove all FISONs from U(F(n)) without changing the claimed union.

Indiction is only ONE of the axioms,

Peano needs more axioms because his approach is very clumsy and dysfunctional. He creates sequences without repetitions - nothing else, let alone numbers. He creates quack, quackquick, quackquickquack, ...
Lorenzen uses: Make a stroke and if you have made x strokes make another stroke. Nothing else than this induction is required to get the natural numbers in the unary system.
Regards, WM