Re: The set of necessary FISONs

WM brought next idea :

On 01.03.2025 19:38, FromTheRafters wrote:

WM presented the following explanation :

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Processes using defined individuals like FISONs cannot surpass a finite set. FISONs are finite. Their number will never be greater than finite.
{1}
{2, 1}
{3, 2, 1}
...

 Those are still not FISONs.

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They are. The order in curly brackets does not matter.

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The term "FISON" stands for "finite initial segment of natural numbers." A FISON is typically defined as a finite set of the form {0,1,2,…,n} for some non-negative integer n.
The set {4,3,2,1} does not meet this definition for a couple of reasons:
    Order: A FISON must include all natural numbers starting from 0 up to n in ascending order. The set {4,3,2,1} is not in ascending order and does not include 0.
    Completeness: A FISON must include all natural numbers less than or equal to its maximum element. In this case, the maximum element is 4, but the set is missing 0.
Therefore, {4,3,2,1} is not a FISON. A valid FISON that includes up to 4 would be {0,1,2,3,4}.