Re: The set of necessary FISONs

On 13.02.2025 13:54, joes wrote:

Am Thu, 13 Feb 2025 12:59:56 +0100 schrieb WM:

All of us who know induction know that by induction we have obtained
that all FISONs can be removed without changing the result.

The result has certainly changed from a nonempty set, whatever
you think the union of inf. many FISONs is.

The assumption was UF = ℕ and has not changed by omitting any FISON.

 

 From the assumption UF = ℕ we have obtained U{ } = { } = ℕ.

With P = „You can leave out A(n) and all preceding FISONs” you get an
infinite number of such sentences, where each leaves infinitely many
FISONs in the union.
 

Induction covers all natural numbers. None is remaining.
Regards, WM