#blairlogicmath search results
Including this surprise reference to hyperbolic geometry. Very fashionable in the arts and literature of the 19th century. Who among us hasn't started talking about negative curvature at a dinner party? #blairlogicmath
The origins of calculus: Fermat’s method of adequality applied to calculating tangent lines. #blairlogicmath
Relative consistency proofs #blairlogicmath
MathOverflow is discussing the question: Are infinitesimal analysis and nonstandard analysis philosophically circular? After all, they make use of standard methods in order to build the nonstandard realm, so how could they replace them? mathoverflow.net/a/438808/1946
This is just great. Casual intro to hyperbolic geometry. #blairlogicmath
from an archive of Open University's M100 course archive.org/details/anoneu… (full list of videos here open.ac.uk/library/digita…, but only a few are on internet archive I think? cc @textfiles )
archive.org
A Non-Euclidean Universe : Open University : Free Download, Borrow,...
Come on over, we're solving differential equations. No not like that, like this. We have some weights, a table, and some curves we already constructed last week. @viktorblasjo tries to teach us what Leibniz was up to in 1693. nieuwarchief.nl/serie5/pdf/naw… #blairlogicmath
Do you hate it when language is inadequate to express yourself with sufficient precision? Have you considered inventing modern predicate logic? That's what I would do, if I were you. #blairlogicmath informationphilosopher.com/solutions/phil…
Another selection from Lectures on the Philosophy of Mathematics. mitpress.mit.edu/books/lectures… #PhilMaths The principle of continuous induction is an induction-like principle that works with the real numbers, and can be used to establish the fundamental theorems of real analysis.
Hyperbolic Geometry puzzle game. This is so good! #blairlogicmath sokyokuban.com
Using formal logic and computer proof checkers to establish equivalents to the parallel postulate with Tarski's geometry axioms. "Parallel postulates and continuity axioms: a mechanized study in intuitionistic logic using Coq." #blairlogicmath hal.inria.fr/hal-01178236v2
The axiom of choice (actually only the axiom of countable choice) is required to show that the union of a countable number of countable sets is countable! #blairlogicmath
I recommend proving first that the countable union of countable sets is countable, and then pointing out implicit use of countable choice, where you choose the particular enumeration of each set. I think this situation clarifies how choice is often used in math without noticing.
The set of rationals < √2 has no least upper bound. Often mentioned, very rarely proved. Well, here it is: youtu.be/UmWppQWTIVA #blairlogicmath
A Coloring Problem Equivalent to the Continuum Hypothesis This is extremely well-written. #blairlogicmath risingentropy.com/a-coloring-pro…
risingentropy.com
A Coloring Problem Equivalent to the Continuum Hypothesis
Summary Is there an infinity in between ℵ0 and 2ℵ0? Is there a way to color the plane with countably many colors so that there are no monochromatic triangles lined up with the x and y axes? If thes…
From the Wikipedia article for Jainism: "Green vegetables and fruits contain uncountable, but not infinite, lives. Dry beans, lentils, cereals, nuts and seeds contain a countable number of lives and their consumption results in the least destruction of life." #blairlogicmath
Do you want an 85-min lecture on a rigorous proof of the Intermediate Value Theorem with only minor errors / misconceptions? You do, I promise. #blairlogicmath youtu.be/SL_7yr8kDkI
The latest podcast by @viktorblasjo on the history and philosophy of Euclid’s Elements is wonderful as usual. intellectualmathematics.com/blog/created-e… #blairlogicmath
Someone who should be more famous: Wanda Montlak Szmielew She seems to be the one who finally clarified the precise relationship between neutral geometry and Euclidean geometry. Initially a student of Tarski's. She lived quite a life! #blairlogicmath mathshistory.st-andrews.ac.uk/Biographies/Sz…
Including this surprise reference to hyperbolic geometry. Very fashionable in the arts and literature of the 19th century. Who among us hasn't started talking about negative curvature at a dinner party? #blairlogicmath
Come on over, we're solving differential equations. No not like that, like this. We have some weights, a table, and some curves we already constructed last week. @viktorblasjo tries to teach us what Leibniz was up to in 1693. nieuwarchief.nl/serie5/pdf/naw… #blairlogicmath
...Gödel's incompleteness theorems, nonstandard models of arithmetic, consistency of ZFC, large cardinal axioms, ... #blairlogicmath
Relative consistency proofs #blairlogicmath
MathOverflow is discussing the question: Are infinitesimal analysis and nonstandard analysis philosophically circular? After all, they make use of standard methods in order to build the nonstandard realm, so how could they replace them? mathoverflow.net/a/438808/1946
A Coloring Problem Equivalent to the Continuum Hypothesis This is extremely well-written. #blairlogicmath risingentropy.com/a-coloring-pro…
risingentropy.com
A Coloring Problem Equivalent to the Continuum Hypothesis
Summary Is there an infinity in between ℵ0 and 2ℵ0? Is there a way to color the plane with countably many colors so that there are no monochromatic triangles lined up with the x and y axes? If thes…
Hyperbolic Geometry puzzle game. This is so good! #blairlogicmath sokyokuban.com
This is just great. Casual intro to hyperbolic geometry. #blairlogicmath
from an archive of Open University's M100 course archive.org/details/anoneu… (full list of videos here open.ac.uk/library/digita…, but only a few are on internet archive I think? cc @textfiles )
archive.org
A Non-Euclidean Universe : Open University : Free Download, Borrow,...
The Axiom of Choice - it's even worse if you don't assume it. #blairlogicmath
In my book, I argue that it is a form of confirmation bias when considering the axiom of choice to look only at the controversial consequences of AC, without also considering the even more bizarre situations that AC rules out. mitpress.mit.edu/books/lectures… #PhilMaths
The axiom of choice (actually only the axiom of countable choice) is required to show that the union of a countable number of countable sets is countable! #blairlogicmath
I recommend proving first that the countable union of countable sets is countable, and then pointing out implicit use of countable choice, where you choose the particular enumeration of each set. I think this situation clarifies how choice is often used in math without noticing.
Do you hate it when language is inadequate to express yourself with sufficient precision? Have you considered inventing modern predicate logic? That's what I would do, if I were you. #blairlogicmath informationphilosopher.com/solutions/phil…
In his attempts to reduce all mathematics to logic—the logicist program—Frege defined the cardinal numbers simply to be these equivalence classes. For Frege, the number 2 is the class of all two-element sets; the number 3 is the class of all three-element sets, and so on.
The latest podcast by @viktorblasjo on the history and philosophy of Euclid’s Elements is wonderful as usual. intellectualmathematics.com/blog/created-e… #blairlogicmath
Do you want an 85-min lecture on a rigorous proof of the Intermediate Value Theorem with only minor errors / misconceptions? You do, I promise. #blairlogicmath youtu.be/SL_7yr8kDkI
My new paper on the early history of the calculus and why formulas were resisted in favour of geometry: link.springer.com/referenceworke…
Another selection from Lectures on the Philosophy of Mathematics. mitpress.mit.edu/books/lectures… #PhilMaths The principle of continuous induction is an induction-like principle that works with the real numbers, and can be used to establish the fundamental theorems of real analysis.
The set of rationals < √2 has no least upper bound. Often mentioned, very rarely proved. Well, here it is: youtu.be/UmWppQWTIVA #blairlogicmath
Why was the discovery by the Ancient Greeks of the irrationality of √2 such a big deal? It threatened their entire analysis of triangle similarity, that proportional sides follow from equal angles. #blairlogicmath
One day I hope to be as cool as Bertrand Russell. Can't believe I've never heard this before... #blairlogicmath via @viktorblasjo
Today in #blairlogicmath we made sad faces in preparation for Tuesday's Gödel's Incompleteness Theorem lecture.
Try to be as proud of your work as Descartes is of his. #blairlogicmath plato.stanford.edu/entries/descar…
What is Mathematics and What Should it Be? by Doron ZEILBERGER arxiv.org/pdf/1704.05560… #blairlogicmath
Come on over, we're solving differential equations. No not like that, like this. We have some weights, a table, and some curves we already constructed last week. @viktorblasjo tries to teach us what Leibniz was up to in 1693. nieuwarchief.nl/serie5/pdf/naw… #blairlogicmath
Reading aloud from Descartes' Discourse on Method in #blairlogicmath and class got a good laugh from the "Chinese or cannibals" line.
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