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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: how
Date: Sat, 13 Apr 2024 08:59:59 -0400
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On 4/13/24 8:23 AM, WM wrote:
> Le 12/04/2024 à 18:58, Richard Damon a écrit :
> 
>> No, "Set Theory" doesn't talk about "differences" based on the values 
>> of the elements, because that is outside of the domain of Set Theory.
> 
> Learn about ordered sets and well-ordered sets. For a start look here 
> https://en.wikipedia.org/wiki/Partially_ordered_set.
> 
> Regrads, WM

Which is MATH THEORY, not SET THEORY (which is a SPECIFIC subset of 
math, DIFFERENT than Order theory).

Read the first words of that reference: In mathematics, especially order 
theory.

The "Set Theory" part of Mathematics doesn't deal with the values, other 
than "equality". Sets themselves are UNORDERED. Other parts of 
Mathematics (like Order Theory) adds concept of "order" to the ELEMENTS 
of the Sets.

And again, it compares SET to SET, not SET to Number.

And "Order Theory" doesn't define "Distance" either, only ordering.

Do the elements of the set have an ordering relationship? And is it strict.