Re: The set of necessary FISONs

Am Thu, 20 Feb 2025 18:50:27 +0100 schrieb WM:

On 20.02.2025 15:30, Jim Burns wrote:
 

AXIOM I 'extensionality' means proving each FISON is omissible  is no
proving {F} is omissible.

∀n ∈ ℕ: n+1 ∈ ℕ. Together with 1 ∈ ℕ this defines the set ℕ. (*)
Addition of all numbers defined by (*) to the empty set is tantamount to
addition of ℕ to the empty set.

Absolutely not. That would be {N}, which is not equal to N = {1, 2,
3, ...}. It would be equal to the addition *of the elements*.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.