Re: The set of necessary FISONs

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

On 02.02.2025 14:47, joes wrote:

Am Sun, 02 Feb 2025 12:43:49 +0100 schrieb WM:

On 02.02.2025 05:55, joes wrote:

Am Sat, 01 Feb 2025 19:23:29 +0100 schrieb WM:

>

Induction proves a sentence for every number, not for the set.
You cannot extend a sentence about numbers to sets.

But to all numbers.

No, to *a* number, though which is arbitrary. Not to a *set* of numbers.

 Mathematical induction is a method for proving that a statement
P(n) is true for every natural number n that is, that the infinitely many cases P(0),P(1),P(2),P(3),... all hold. [Wikipedia]
 

Yes, and it has rules and proceedure that you don't seem to understand, and which it doesn't appear your logic allows.

Peano does not describe the set ℕ?

N is not a natural number.

 Not described by the Peano axioms?

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

>

Anyhow all natural numbers n and all A(n) are discarded.

No, there are more than any finite number.

 Name one?

Greater than the number n are n+1, n+2, n+3, n+4, ...
SInce your logic only does things individually, you can't handle an "all" with it.

 Regards, WM