Re: The set of necessary FISONs

FromTheRafters pretended :

It happens that WM formulated :

On 26.01.2025 23:31, Richard Damon wrote:

On 1/26/25 9:28 AM, WM wrote:

>

>

{1}
{2, 1}
{3, 2, 1}
...
>
The first column never gets larger than a FISON.

 Sure it does,

>
Finite Initial Segments Of Natural numbers remain finite by definition.

>
They also have the natural order of the natural numbers. Even you apparently say so.

See "Ordered "sequence" below.
From Google's AI:
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AI Overview
In set theory, a "FISON" stands for "Finite Initial Segment Of Natural Numbers" - it refers to a set containing the first 'n' natural numbers (1, 2, 3, ..., n) where 'n' is any finite positive integer; essentially, a small, finite subset of the set of all natural numbers.
Key points about FISONs:
    Finite nature:
    A FISON is always a finite set, meaning it has a limited number of elements.
    Ordered sequence:
    The elements within a FISON are always listed in their natural order (from 1 to n).
    Example:
    The set {1, 2, 3, 4, 5} is a FISON, representing the first five natural numbers.
Use in mathematical concepts:
    Induction proofs: FISONs are often used in mathematical induction proofs where you need to demonstrate a property holds for all natural numbers by showing it holds for the first element, then assuming it holds for any element 'n' and proving it holds for 'n+1'.
    Dark numbers
    Dark natural numbers proved by the sequence of FISONs According to set theory the set ع of all natural numbers is actually infinit...
    Technische Hochschule Augsburg
Generative AI is experimental.
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Technische Hochschule Augsburg is polluting Google's AI. It makes me wonder what either entity thinks about that. :)