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

[Larry Wittig]

This is interesting. Chat gave a much more useful answer than the one
I sent out from Wikipedia.  Chat has trouble with doing math -- it
stumbled on a two unknowns algebra problem I gave it a while back.
But gave what appears to be a very good answer about a mathematical
concept.

On Sat, Nov 18, 2023 at 10:56 PM John Rudy via LCTG <lctg at lists.toku.us> wrote:
>
> 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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