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

[palbin24 at yahoo.com]

Ok, I too went to Wikipedia and my eyes glazed over. Hence my question to the group.

Chat’s response is clearer, but begs the question: is this an academic exercise or is there a practical use?
Also, so D(9) is a large number; what does that mean? Is this akin to finding the largest prime number?

Peter

> On Nov 19, 2023, at 11:47 AM, Larry Wittig <9423lew at gmail.com> wrote:
> 
> 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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