[Lex Computer & Tech Group/LCTG] Mathematicians Have Found The Ninth Dedekind Number, After 32 Years of Searching

[jjrudy1 at comcast.net]

I went to ChatGPT:
==========================   

explain Dedekind Number in simple words
ChatGPT
A Dedekind number is a way to count how "big" a certain set is, specifically
in the realm of mathematics. Named after the German mathematician Richard
Dedekind, these numbers are used to measure the size or cardinality of
infinite sets.

Here's a simple way to understand it:

Imagine you have an infinite set of objects, like all the natural numbers
(1, 2, 3, and so on). Now, think about dividing this set into two parts in a
specific way: one part contains only the odd numbers, and the other part
contains the even numbers. Surprisingly, even though both sets are infinite,
they have the same size! In mathematical terms, we say that the set of
natural numbers can be "bijected" or paired up with the set of even numbers.

The Dedekind number comes into play when we want to compare the sizes of
different infinite sets. Each Dedekind number corresponds to a specific way
of dividing an infinite set into two parts. If two sets can be paired up in
such a way that no elements are left out, and no elements are repeated, then
they are considered to have the same size, or cardinality, and share the
same Dedekind number.

In essence, Dedekind numbers help mathematicians talk about the sizes of
infinite sets and understand the different ways in which these sets can be
compared or related.






-----Original Message-----
From: LCTG <lctg-bounces+jjrudy1=comcast.net at lists.toku.us> On Behalf Of
Peter Albin via LCTG
Sent: Saturday, November 18, 2023 9:31 PM
To: Lex Computer Group <lctg at lists.toku.us>
Subject: [Lex Computer & Tech Group/LCTG] Mathematicians Have Found The
Ninth Dedekind Number, After 32 Years of Searching


https://www.sciencealert.com/mathematicians-have-found-the-ninth-dedekind-nu
mber-after-32-years-of-searching

Now, can someone explain what a Dedekind Number is in English? Is it worth a
session?

Peter
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