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njwildberger: tangential thoughts | mathematical ruminations and more

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njwildberger: tangential thoughts | mathematical ruminations and more | njwildberger.com Reviews

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Space-filling curves do not exist | njwildberger: tangential thoughts

https://njwildberger.com/2016/01/22/space-filling-curves-do-not-exist

Mathematical ruminations and more. Space-filling curves do not exist. When does ideology trump common sense? This question is very relevant to the sad situation with modern pure mathematics, which is in a dire logical mess. All manner of dubious concepts and arguments are floating around out there, sustained by our fervent desire that the limiting operations underlying modern analysis actually make sense. We must believe — we will believe! And there is hardly a more obviously suspicious case than that of.

2

Some fundamental formulas from metrical algebraic geometry (seminar) | njwildberger: tangential thoughts

https://njwildberger.com/2015/06/06/some-fundamental-formulas-of-metrical-algebraic-geometry-seminar

Mathematical ruminations and more. Some fundamental formulas from metrical algebraic geometry (seminar). This coming Tuesday in the Pure Maths Seminar at UNSW I will be giving a talk: Here are the details, in case you are in Sydney and are interested. The talk is at the School of Mathematics and Statistics, UNSW, Kensington campus, building the Red Centre, which is up the main walkway from Anzac Parade. Speaker: Norman Wildberger (UNSW). Title: Some fundamental formulas from metrical algebraic geometry.

3

My future glorious life! | njwildberger: tangential thoughts

https://njwildberger.com/2014/10/29/my-future-glorious-life

Mathematical ruminations and more. My future glorious life! I am so excited! Here drinking my morning green tea, i have just been visited by an image of St. Peter, who proclaimed to me that all my personal dreams are about to come true, provided i can write them down on this blog in the next half an hour! He said I couldn’t actually change my physical characteristics, so I reckon that beyond 100, frailty is too much of an issue. But I’m wasting time explaining these things to you! And a villa in Tuscany&...

4

Conceptual versus rhetorical definitions | njwildberger: tangential thoughts

https://njwildberger.com/2016/01/17/conceptual-versus-rhetorical-definitions

Mathematical ruminations and more. Conceptual versus rhetorical definitions. Here are two definitions, both taken from the internet. Definition 1: A dog. Is a domesticated carnivorous mammal that typically has a long snout, an acute sense of smell, non-retractile claws, and a barking, howling, or whining voice. Definition 2: An encumbered asset. Is one that is currently being used as security or collateral for a loan. While others merely package conveniently and concisely. What we already know. This migh...

5

Let alpha be a real number | njwildberger: tangential thoughts

https://njwildberger.com/2015/12/07/let-alpha-be-a-real-number

Mathematical ruminations and more. Let alpha be a real number. PM (Pure Mathematician): Let alpha be a real number. NJ (Me): What does that mean? PM: Surely you are joking. What do you mean by such a question? Everyone uses this phrase all the time, probably you also. NJ: I used to, but now I am not so sure anymore what it means. In fact I suspect it is nonsense. So I am asking you to clarify its meaning for me. NJ: Is that a real number, or just a few decimal digits followed by three dots? But now that ...

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Groupoids | Gentzen translated

https://gentzen.wordpress.com/2015/08/03/groupoids

Reversibility of binary relations, substochastic matrices, and partial functions. On Zeros of a Polynomial in a Finite Grid: the Alon-Furedi bound →. August 3, 2015. My current top candidate for a mathematical concept that should be and is not (as far as I can tell) consistently taught at the advanced undergraduate / beginning graduate level is the notion of a groupoid. Today’s post is a very brief introduction to groupoids together with some suggestions for further reading. 1,848 more words. The more tr...

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Gentzen’s consistency proof is more impressive than you expect | Gentzen translated

https://gentzen.wordpress.com/2013/12/05/gentzens-consistency-proof-is-more-impressive-than-you-expect

Algebraic characterizations of inverse semigroups and strongly regular rings →. Gentzen’s consistency proof is more impressive than you expect. December 5, 2013. I recently said something. About the impossibility to prove the consistency of PA, and that Gentzen proved just this in 1936. Because I got critizised quite a bit, and realized that even famous mathematicians get critizized. If they dare to mention. Logic, Logic, and Logic. View all posts by gentzen →. This entry was posted in logic. If I rememb...

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About | Gentzen translated

https://gentzen.wordpress.com/about

If you need to contact me privately, you can try. Jacques dot gentzen at gmail dot com. Volker Diekert, Manfred Kufleitner, Gerhard Rosenberger: “Diskrete algebraische Methoden: Arithmetik, Kryptographie, Automaten und Gruppen”. And Heinz-Dieter Ebbinghaus, Jörg Flum, Wolfgang Thomas: “Einführung in die mathematische Logik”. I cite these books, because they managed to teach me advanced material, which I already tried to learn with less success before. January 26, 2016 at 10:44 pm. Thx for the link! Ajit ...

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gentzen | Gentzen translated

https://gentzen.wordpress.com/author/gentzen

Logic, Logic, and Logic. September 3, 2016. It is neither new, nor complicated enough to count as real math! And suggestions that or might be even better show that it not clear-cut either. I recently invested sufficient energy into some logical questions to … Continue reading →. Learning category theory: a necessary evil? April 3, 2016. A canonical labeling technique by Brendan McKay and isomorphism testing of deterministic finite automata. November 15, 2015. September 19, 2015. August 3, 2015. My curren...

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Algebraic characterizations of inverse semigroups and strongly regular rings | Gentzen translated

https://gentzen.wordpress.com/2014/12/06/algebraic-characterizations-of-inverse-semigroups-and-strongly-regular-rings

Gentzen’s consistency proof is more impressive than you expect. Reversibility of binary relations, substochastic matrices, and partial functions →. Algebraic characterizations of inverse semigroups and strongly regular rings. December 6, 2014. A good place to learn about inverse semigroups are Tero Harju’s Lecture Notes on Semigroups. The real text is in a short pdf. The original proofs were mostly found via google, but after a conversation with a real guru. Input files. The companion program mace4 t...

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Reversibility of binary relations, substochastic matrices, and partial functions | Gentzen translated

https://gentzen.wordpress.com/2015/03/22/reversibility-of-binary-relations-substochastic-matrices-and-partial-functions

Algebraic characterizations of inverse semigroups and strongly regular rings. Reversibility of binary relations, substochastic matrices, and partial functions. March 22, 2015. After the last post, I decided that the next post should contain images. Next I decided that the time to publish another post has come. Here is an image of an acceptor finite-state machine. Parsing the string “nice”. How can we revert this machine, such that it parses the string “ecin”? Is a very nice book. Its chapter 7. Similarit...

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njwildberger: tangential thoughts | mathematical ruminations and more

Mathematical ruminations and more. Upcoming talk on the Goldbach Conjecture. Some exciting news, I will next month be giving a talk which, amongst other things, will resolve the Goldbach Conjecture. That is a rather famous conjecture in Number Theory that asserts that every even number can be written as the sum of two primes. The talk will be in the Pure Mathematics Colloquium on November 8 2016. Speaker: A/Prof N J Wildberger (UNSW). We will also bump into philosophical questions about the true nature o...

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