Re: The set of necessary FISONs

On 04.02.2025 13:17, Richard Damon wrote:

On 2/4/25 5:50 AM, WM wrote:

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.

 Which just proves that all F(n) are in the set that can be individually not needed.

Then they all F(n) together can be individually discarded. Just like all natural numbers together can be discarded by subtracting them.

 

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.

 Which doesn't CREATE the set N, it shows that some other set is N.

If there is another set, then we could use it without need of Peano.
Regards, WM