Re: The set of necessary FISONs

On 04.02.2025 01:39, Richard Damon wrote:

On 2/3/25 7:45 AM, WM wrote:

On 02.02.2025 21:11, Richard Damon wrote:

On 2/2/25 11:39 AM, WM wrote:

describe the set ℕ?

N is not a natural number.

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Not described by the Peano axioms?

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You seem to not understand the differnce between a number and a set of numbers

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Peano creates by induction the set ℕ of all natural numbers.
Why doe I not delete by the same induction the set of all FISONs?

Because you don't prove the needed induction.
 You prove that no individual F(n) is needed.

F(1) can be subtracted, and if F(n) can be subtracted, then F(n+1) can be subtracted. That is the needed induction.

Note also, Peano doesn't "create" the Naturals with induction,

He does. 1 or 0 ∈ ℕ, and if n is there, then n' is there.
Regards, WM