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

Sun Nov 19 14:00:50 PST 2023

Have you tried comparing the results in chat GPT 3.5 to what the chat GPT 4.0 results are?

Bing chat is 4.0 so you can enter the same query there and compare the two results.

There's even a Bing chat mobile app that works really well.

-- 
Drew King

On November 19, 2023 4:11:28 PM EST, Peter Albin via LCTG <lctg at lists.toku.us> wrote:
>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
>>> ===============================================
>>> ::The Lexington Computer and Technology Group Mailing List::
>>> Reply goes to sender only; Reply All to send to list.
>>> Send to the list: LCTG at lists.toku.us      Message archives:
>>> http://lists.toku.us/pipermail/lctg-toku.us/
>>> To subscribe: email lctg-subscribe at toku.us  To unsubscribe: email
>>> lctg-unsubscribe at toku.us Future and Past meeting information:
>>> http://LCTG.toku.us List information:
>>> http://lists.toku.us/listinfo.cgi/lctg-toku.us
>>> This message was sent to jjrudy1 at comcast.net.
>>> Set your list options:
>>> http://lists.toku.us/options.cgi/lctg-toku.us/jjrudy1@comcast.net
>>> 
>>> ===============================================
>>> ::The Lexington Computer and Technology Group Mailing List::
>>> Reply goes to sender only; Reply All to send to list.
>>> Send to the list: LCTG at lists.toku.us      Message archives: http://lists.toku.us/pipermail/lctg-toku.us/
>>> To subscribe: email lctg-subscribe at toku.us  To unsubscribe: email lctg-unsubscribe at toku.us
>>> Future and Past meeting information: http://LCTG.toku.us
>>> List information: http://lists.toku.us/listinfo.cgi/lctg-toku.us
>>> This message was sent to 9423lew at gmail.com.
>>> Set your list options: http://lists.toku.us/options.cgi/lctg-toku.us/9423lew@gmail.com
>
>===============================================
>::The Lexington Computer and Technology Group Mailing List::
>Reply goes to sender only; Reply All to send to list.
>Send to the list: LCTG at lists.toku.us      Message archives: http://lists.toku.us/pipermail/lctg-toku.us/
>To subscribe: email lctg-subscribe at toku.us  To unsubscribe: email lctg-unsubscribe at toku.us
>Future and Past meeting information: http://LCTG.toku.us
>List information: http://lists.toku.us/listinfo.cgi/lctg-toku.us
>This message was sent to dking65 at kingconsulting.us.
>Set your list options: http://lists.toku.us/options.cgi/lctg-toku.us/dking65@kingconsulting.us
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.toku.us/pipermail/lctg-toku.us/attachments/20231119/88f46ae4/attachment.htm>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Bingchat is4. 0.jpg
Type: image/jpeg
Size: 268226 bytes
Desc: not available
URL: <http://lists.toku.us/pipermail/lctg-toku.us/attachments/20231119/88f46ae4/attachment.jpg>