#BooleanAlgebra

David WilkinsYesterday on a visit to Lincoln, I came across this highly informative memorial to one of the city’s most distinguished sons, the mathematician George Boole - as in Boolean logic/algebra - described here as the grandfather of the digital age.<a href="https://mastodon.online/tags/GeorgeBoole" class="mention hashtag" rel="nofollow noopener" target="_blank">#GeorgeBoole</a> <a href="https://mastodon.online/tags/BooleanLogic" class="mention hashtag" rel="nofollow noopener" target="_blank">#BooleanLogic</a> <a href="https://mastodon.online/tags/BooleanAlgebra" class="mention hashtag" rel="nofollow noopener" target="_blank">#BooleanAlgebra</a> <a href="https://mastodon.online/tags/dwprovinvialbritain" class="mention hashtag" rel="nofollow noopener" target="_blank">#dwprovinvialbritain</a>

Inquiry Into InquiryDifferential Propositional Calculus • 10Special Classes of Propositions (cont.)Let’s pause at this point and get a better sense of how our special classes of propositions are structured and how they relate to propositions in general.  We can do this by recruiting our visual imaginations and drawing up a sufficient budget of venn diagrams for each family of propositions.  The case for 3 variables is exemplary enough for a start.Linear PropositionsThe <a href="https://inquiryintoinquiry.com/wp-content/uploads/2020/02/linear-propositions-may-be-written-as-sums.png" rel="nofollow noopener" target="_blank">linear propositions</a>, may be written as sums:One thing to keep in mind about these sums is that the values in are added “modulo 2”, that is, in such a way that In a universe of discourse based on three boolean variables, the linear propositions take the shapes shown in Figure 8.<a href="https://inquiryintoinquiry.com/wp-content/uploads/2020/02/venn-diagrams-e280a2-p-q-r-e280a2-linear-propositions.jpg" rel="nofollow noopener" target="_blank"></a> At the top is the venn diagram for the linear proposition of rank 3, which may be expressed by any one of the following three forms.Next are the venn diagrams for the three linear propositions of rank 2, which may be expressed by the following three forms, respectively.Next are the three linear propositions of rank 1, which are none other than the three basic propositions, At the bottom is the linear proposition of rank 0, the everywhere false proposition or the constant function, which may be expressed by the form or by a simple Resources<ul><li><a href="https://inquiryintoinquiry.com/logic-syllabus/" rel="nofollow noopener" target="_blank">Logic Syllabus</a></li><li><a href="https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7/" rel="nofollow noopener" target="_blank">Survey of Differential 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Your Autistic Life FR/EN/ESBoolean algebra, my nemesis! We meet again!I'm going to tutor in Boolean algebra in about 30 minutes.Actually, it is not a nemesis. Boolean algebra is the one "algebra" that I would have been able to tutor last year before I started refreshing my memory of the other types of algebra. I never really ceased using it.Ask me to factor a polynomial last year, however, and you would have gotten a blank stare. The last time I did any of that was over 30 years ago. 😬 (Happy to report that I took care of refreshing my memory.)<a href="https://mast.yourautisticlife.com/tags/tutorig" class="mention hashtag" rel="nofollow noopener" target="_blank">#tutorig</a> <a href="https://mast.yourautisticlife.com/tags/boolean" class="mention hashtag" rel="nofollow noopener" target="_blank">#boolean</a> <a href="https://mast.yourautisticlife.com/tags/BooleanAlgebra" class="mention hashtag" rel="nofollow noopener" target="_blank">#BooleanAlgebra</a> <a href="https://mast.yourautisticlife.com/tags/BooleanLogic" class="mention hashtag" rel="nofollow noopener" target="_blank">#BooleanLogic</a> <a href="https://mast.yourautisticlife.com/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mast.yourautisticlife.com/tags/logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#logic</a>

Irish Philosophy<a href="https://mastodon.ie/tags/GeorgeBoole" class="mention hashtag" rel="nofollow noopener" target="_blank">#GeorgeBoole</a> (1815–64), mathematician, was born <a href="https://mastodon.ie/tags/OTD" class="mention hashtag" rel="nofollow noopener" target="_blank">#OTD</a> 1815 at Lincoln.Largely self-taught, he became professor of <a href="https://mastodon.ie/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathematics</a> in the Royal College Cork (the forerunner of <a href="https://mastodon.ie/tags/UCC" class="mention hashtag" rel="nofollow noopener" target="_blank">#UCC</a>) and worked there there until his death.DIB: <a href="https://www.dib.ie/biography/boole-george-a0780" rel="nofollow noopener" translate="no" target="_blank">https://www.dib.ie/biography/boole-george-a0780</a>His work which underlies computer programs was originally applied to test the validity of Spinoza's thought.Ones and Zeros: the life and work of George Boole<a href="https://www.irishphilosophy.com/2014/12/08/ones-and-zeros/" rel="nofollow noopener" translate="no" target="_blank">https://www.irishphilosophy.com/2014/12/08/ones-and-zeros/</a><a href="https://mastodon.ie/tags/IrishPhilosophyOTD" class="mention hashtag" rel="nofollow noopener" target="_blank">#IrishPhilosophyOTD</a> <a href="https://mastodon.ie/tags/HistoryOfMaths" class="mention hashtag" rel="nofollow noopener" target="_blank">#HistoryOfMaths</a> <a href="https://mastodon.ie/tags/BooleanAlgebra" class="mention hashtag" rel="nofollow noopener" target="_blank">#BooleanAlgebra</a>

Jon AwbreySurvey of Animated Logical Graphs • <a href="https://inquiryintoinquiry.com/2023/03/28/survey-of-animated-logical-graphs-5/" rel="nofollow noopener" target="_blank">https://inquiryintoinquiry.com/2023/03/28/survey-of-animated-logical-graphs-5/</a>This is a Survey of blog and wiki posts on Logical Graphs, encompassing several families of graph-theoretic structures originally developed by Charles S. Peirce as graphical formal languages or visual styles of syntax amenable to interpretation for logical applications.<a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="nofollow noopener" target="_blank">#Peirce</a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#Logic</a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#LogicalGraphs</a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#EntitativeGraphs</a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#ExistentialGraphs</a> <a href="https://mathstodon.xyz/tags/Boole" class="mention hashtag" rel="nofollow noopener" target="_blank">#Boole</a> <a href="https://mathstodon.xyz/tags/BooleanAlgebra" class="mention hashtag" rel="nofollow noopener" target="_blank">#BooleanAlgebra</a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="nofollow noopener" target="_blank">#BooleanFunctions</a> <a href="https://mathstodon.xyz/tags/ModelTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#ModelTheory</a> <a href="https://mathstodon.xyz/tags/ProofTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#ProofTheory</a> <a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="nofollow noopener" target="_blank">#SpencerBrown</a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="nofollow noopener" target="_blank">#LawsOfForm</a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="nofollow noopener" target="_blank">#PropositionalCalculus</a> <a href="https://mathstodon.xyz/tags/LogicAsSemiotics" class="mention hashtag" rel="nofollow noopener" target="_blank">#LogicAsSemiotics</a>

Oscar CunninghamBut in fact, the complete atomic boolean algebras are precisely the same as the *completely distributive* boolean algebras. These are the algebras for which all infinite joins and meets exist, and the two infinitary operations distribute over each other.That's a much more natural property! People should state the theorem with CDBAs and not CABAs! (2/2)<a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#CategoryTheory</a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Mathematics</a> <a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="nofollow noopener" target="_blank">#Math</a> <a href="https://mathstodon.xyz/tags/Maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#Maths</a> <a href="https://mathstodon.xyz/tags/BooleanAlgebra" class="mention hashtag" rel="nofollow noopener" target="_blank">#BooleanAlgebra</a>

Cork Coast 🌊📷🪫<a href="https://mastodon.ie/tags/tombTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#tombTuesday</a> George Boole, <a href="https://mastodon.ie/tags/cork" class="mention hashtag" rel="nofollow noopener" target="_blank">#cork</a><a href="https://en.wikipedia.org/wiki/George_Boole?wprov=sfla1" rel="nofollow noopener" target="_blank">https://en.wikipedia.org/wiki/George_Boole?wprov=sfla1</a><a href="https://mastodon.ie/tags/boolean" class="mention hashtag" rel="nofollow noopener" target="_blank">#boolean</a> <a href="https://mastodon.ie/tags/programming" class="mention hashtag" rel="nofollow noopener" target="_blank">#programming</a> <a href="https://mastodon.ie/tags/ucc" class="mention hashtag" rel="nofollow noopener" target="_blank">#ucc</a> <a href="https://mastodon.ie/tags/booleanAlgebra" class="mention hashtag" rel="nofollow noopener" target="_blank">#booleanAlgebra</a> <a href="https://mastodon.ie/tags/oldCork" class="mention hashtag" rel="nofollow noopener" target="_blank">#oldCork</a> <a href="https://mastodon.ie/tags/oldCorkPhotos" class="mention hashtag" rel="nofollow noopener" target="_blank">#oldCorkPhotos</a> <a href="https://mastodon.ie/tags/computerScience" class="mention hashtag" rel="nofollow noopener" target="_blank">#computerScience</a>

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#booleanalgebra