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<div dir="ltr" data-setdir="false">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:</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">First, let's have a clear understanding that Dedekind Cuts in Set Theory are related to the Dedekind Numbers in Number Theory. </div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false"><span>ELI5: the 9th Dedekind number has just been discovered. What are Dedekind numbers?</span><br></div><div dir="ltr" data-setdir="false"><a href="https://www.reddit.com/r/explainlikeimfive/comments/14pt3dt/eli5_the_9th_dedekind_number_has_just_been/?rdt=58457" rel="nofollow" target="_blank">https://www.reddit.com/r/explainlikeimfive/comments/14pt3dt/eli5_the_9th_dedekind_number_has_just_been/?rdt=58457</a> <span><br></span></div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">Applications to space-time concepts are summarized in this Stack Exchange entry:</div><div dir="ltr" data-setdir="false"><span>Do Cauchy Sequences and Dedekind cuts have any real-world applications?</span><br></div><div dir="ltr" data-setdir="false"><a href="https://math.stackexchange.com/questions/4014126/do-cauchy-sequences-and-dedekind-cuts-have-any-real-world-applications" rel="nofollow" target="_blank">https://math.stackexchange.com/questions/4014126/do-cauchy-sequences-and-dedekind-cuts-have-any-real-world-applications</a> <span><br></span></div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">The long form of the body of Dedekind's work and its relationships to Number Theory and Set Theory are summarized in this article:</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false"><span>Dedekind’s Contributions to the Foundations of Mathematics</span><br></div><div dir="ltr" data-setdir="false"><span><span>Stanford Encyclopedia of Philosophy</span><br></span></div><div dir="ltr" data-setdir="false"><a href="https://plato.stanford.edu/entries/dedekind-foundations/" rel="nofollow" target="_blank">https://plato.stanford.edu/entries/dedekind-foundations/</a> <span><span><br></span></span></div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">Are we any closer to a plain-English understanding of what the Dedekind Numbers are able to tell us about the Real World now?</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">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. </div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">-- Bob P}rimak</div><div dir="ltr" data-setdir="false"><br></div>
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On Sunday, November 19, 2023 at 10:17:15 PM EST, George Gamota via LCTG <lctg@lists.toku.us> wrote:
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<div><div dir="ltr">I am sorry but this does not sound like English...<br clear="none">George<br clear="none"><br clear="none">-----Original Message-----<br clear="none">From: LCTG <lctg-bounces+ggamota=stma-llc.com@lists.toku.us> On Behalf Of Larry Wittig via LCTG<br clear="none">Sent: Sunday, November 19, 2023 11:36 AM<br clear="none">To: <a shape="rect" ymailto="mailto:palbin24@yahoo.com" href="mailto:palbin24@yahoo.com">palbin24@yahoo.com</a><br clear="none">Cc: Lex Computer Group <<a shape="rect" ymailto="mailto:lctg@lists.toku.us" href="mailto:lctg@lists.toku.us">lctg@lists.toku.us</a>><br clear="none">Subject: Re: [Lex Computer & Tech Group/LCTG] Mathematicians Have Found The Ninth Dedekind Number, After 32 Years of Searching<br clear="none"><br clear="none">The Dedekind numbers are a rapidly growing sequence of integers named after Richard Dedekind, who defined them in 1897. The Dedekind number<br clear="none">M(n) is the number of monotone boolean functions of n variables.<br clear="none">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.<br clear="none"><br clear="none"><br clear="none">On Sat, Nov 18, 2023 at 9:33 PM Peter Albin via LCTG <<a shape="rect" ymailto="mailto:lctg@lists.toku.us" href="mailto:lctg@lists.toku.us">lctg@lists.toku.us</a>> wrote:<br clear="none">><br clear="none">><br clear="none">> <a shape="rect" href="https://www.sciencealert.com/mathematicians-have-found-the-ninth-dedek" target="_blank">https://www.sciencealert.com/mathematicians-have-found-the-ninth-dedek</a><br clear="none">> ind-number-after-32-years-of-searching<br clear="none">><br clear="none">> Now, can someone explain what a Dedekind Number is in English? Is it worth a session?<br clear="none">><br clear="none">> Peter<br clear="none">> ===============================================<br clear="none">> ::The Lexington Computer and Technology Group Mailing List::<br clear="none">> Reply goes to sender only; Reply All to send to list.<br clear="none">> Send to the list: <a shape="rect" ymailto="mailto:LCTG@lists.toku.us" href="mailto:LCTG@lists.toku.us">LCTG@lists.toku.us</a> Message archives: <a shape="rect" href="http://lists.toku.us/pipermail/lctg-toku.us/" target="_blank">http://lists.toku.us/pipermail/lctg-toku.us/</a><br clear="none">> To subscribe: email <a shape="rect" ymailto="mailto:lctg-subscribe@toku.us" href="mailto:lctg-subscribe@toku.us">lctg-subscribe@toku.us</a> To unsubscribe: email <br clear="none">> <a shape="rect" ymailto="mailto:lctg-unsubscribe@toku.us" href="mailto:lctg-unsubscribe@toku.us">lctg-unsubscribe@toku.us</a> Future and Past meeting information: <br clear="none">> <a shape="rect" href="http://LCTG.toku.us" target="_blank">http://LCTG.toku.us</a> List information: <br clear="none">> <a shape="rect" href="http://lists.toku.us/listinfo.cgi/lctg-toku.us" target="_blank">http://lists.toku.us/listinfo.cgi/lctg-toku.us</a><br clear="none">> This message was sent to <a shape="rect" ymailto="mailto:9423lew@gmail.com." href="mailto:9423lew@gmail.com.">9423lew@gmail.com.</a><br clear="none">> Set your list options: <br clear="none">> <a shape="rect" href="http://lists.toku.us/options.cgi/lctg-toku.us/9423lew@gmail.com" target="_blank">http://lists.toku.us/options.cgi/lctg-toku.us/9423lew@gmail.com</a><br clear="none">===============================================<br clear="none">::The Lexington Computer and Technology Group Mailing List::<br clear="none">Reply goes to sender only; Reply All to send to list.<br clear="none">Send to the list: <a shape="rect" ymailto="mailto:LCTG@lists.toku.us" href="mailto:LCTG@lists.toku.us">LCTG@lists.toku.us</a> Message archives: <a shape="rect" href="http://lists.toku.us/pipermail/lctg-toku.us/" target="_blank">http://lists.toku.us/pipermail/lctg-toku.us/</a><br clear="none">To subscribe: email <a shape="rect" ymailto="mailto:lctg-subscribe@toku.us" href="mailto:lctg-subscribe@toku.us">lctg-subscribe@toku.us</a> To unsubscribe: email <a shape="rect" ymailto="mailto:lctg-unsubscribe@toku.us" href="mailto:lctg-unsubscribe@toku.us">lctg-unsubscribe@toku.us</a> Future and Past meeting information: <a shape="rect" href="http://LCTG.toku.us" target="_blank">http://LCTG.toku.us</a> List information: <a shape="rect" href="http://lists.toku.us/listinfo.cgi/lctg-toku.us" target="_blank">http://lists.toku.us/listinfo.cgi/lctg-toku.us</a><br clear="none">This message was sent to <a shape="rect" ymailto="mailto:ggamota@stma-llc.com." href="mailto:ggamota@stma-llc.com.">ggamota@stma-llc.com.</a><br clear="none">Set your list options: <a shape="rect" href="http://lists.toku.us/options.cgi/lctg-toku.us/ggamota@stma-llc.com" target="_blank">http://lists.toku.us/options.cgi/lctg-toku.us/ggamota@stma-llc.com</a><div class="yqt9371942646" id="yqtfd96196"><br clear="none"><br clear="none">===============================================<br clear="none">::The Lexington Computer and Technology Group Mailing List::<br clear="none">Reply goes to sender only; Reply All to send to list.<br clear="none">Send to the list: <a shape="rect" ymailto="mailto:LCTG@lists.toku.us" href="mailto:LCTG@lists.toku.us">LCTG@lists.toku.us</a> Message archives: <a shape="rect" href="http://lists.toku.us/pipermail/lctg-toku.us/" target="_blank">http://lists.toku.us/pipermail/lctg-toku.us/</a><br clear="none">To subscribe: email <a shape="rect" ymailto="mailto:lctg-subscribe@toku.us" href="mailto:lctg-subscribe@toku.us">lctg-subscribe@toku.us</a> To unsubscribe: email <a shape="rect" ymailto="mailto:lctg-unsubscribe@toku.us" href="mailto:lctg-unsubscribe@toku.us">lctg-unsubscribe@toku.us</a><br clear="none">Future and Past meeting information: <a shape="rect" href="http://LCTG.toku.us" target="_blank">http://LCTG.toku.us</a><br clear="none">List information: <a shape="rect" href="http://lists.toku.us/listinfo.cgi/lctg-toku.us" target="_blank">http://lists.toku.us/listinfo.cgi/lctg-toku.us</a><br clear="none">This message was sent to <a shape="rect" ymailto="mailto:bobprimak@yahoo.com." href="mailto:bobprimak@yahoo.com.">bobprimak@yahoo.com.</a><br clear="none">Set your list options: <a shape="rect" href="http://lists.toku.us/options.cgi/lctg-toku.us/bobprimak@yahoo.com" target="_blank">http://lists.toku.us/options.cgi/lctg-toku.us/bobprimak@yahoo.com</a><br clear="none"></div></div></div>
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