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

[Robert Primak]

 The short form of where the Dedekind Numbers fit into practical applications of Number Theory and Set Theory (and the physics of space-time) are well summarized here:
First, let's have a clear understanding that Dedekind Cuts in Set Theory are related to the Dedekind Numbers in Number Theory. 
ELI5: the 9th Dedekind number has just been discovered. What are Dedekind numbers?
https://www.reddit.com/r/explainlikeimfive/comments/14pt3dt/eli5_the_9th_dedekind_number_has_just_been/?rdt=58457 

Applications to space-time concepts are summarized in this Stack Exchange entry:Do Cauchy Sequences and Dedekind cuts have any real-world applications?
https://math.stackexchange.com/questions/4014126/do-cauchy-sequences-and-dedekind-cuts-have-any-real-world-applications 

The long form of the body of Dedekind's work and its relationships to Number Theory and Set Theory are summarized in this article:
Dedekind’s Contributions to the Foundations of Mathematics
Stanford Encyclopedia of Philosophy
https://plato.stanford.edu/entries/dedekind-foundations/ 

Are we any closer to a plain-English understanding of what the Dedekind Numbers are able to tell us about the Real World now?
I confess, I am anything but an expert on mathematics and the theory of numbers or sets. So I can only just graze the surface of this very advanced topic. 
-- Bob P}rimak
    On Sunday, November 19, 2023 at 10:17:15 PM EST, George Gamota via LCTG <lctg at lists.toku.us> wrote:  
 
 I am sorry but this does not sound like English...
George

-----Original Message-----
From: LCTG <lctg-bounces+ggamota=stma-llc.com at lists.toku.us> On Behalf Of Larry Wittig via LCTG
Sent: Sunday, November 19, 2023 11:36 AM
To: palbin24 at yahoo.com
Cc: Lex Computer Group <lctg at lists.toku.us>
Subject: Re: [Lex Computer & Tech Group/LCTG] Mathematicians Have Found The Ninth Dedekind Number, After 32 Years of Searching

The Dedekind numbers are a rapidly growing sequence of integers named after Richard Dedekind, who defined them in 1897. The Dedekind number
M(n) is the number of monotone boolean functions of n variables.
Equivalently, it is the number of antichains of subsets of an n-element set, the number of elements in a free distributive lattice with n generators, and one more than the number of abstract simplicial complexes on a set with n elements.


On Sat, Nov 18, 2023 at 9:33 PM Peter Albin via LCTG <lctg at lists.toku.us> wrote:
>
>
> https://www.sciencealert.com/mathematicians-have-found-the-ninth-dedek
> ind-number-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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