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mathenchant.wordpress.com | ||
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micromath.wordpress.com
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| | | | | Continuing the theme of alternative approaches to teaching calculus, I take the liberty of posting a letter sent by Donald Knuth to to the Notices of the American Mathematical Society in March, 1998 (TeX file). Professor Anthony W. Knapp P O Box 333 East Setauket, NY 11733 Dear editor, I am pleased to see so... | |
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math.andrej.com
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| | | | | [AI summary] The discussion revolves around the nuances of proof methods in constructive mathematics, particularly the distinction between proof by contradiction and proof by negation. Key points include the definition of irrational numbers without relying on the law of excluded middle, the use of contrapositive in proofs, and the limitations of certain classical theorems like the intermediate value theorem in constructive settings. The conversation also touches on the philosophical and practical implications of these proof methods in both classical and intuitionistic logic, as well as the role of type theory and univalent foundations in modern mathematical proofs. | |
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divisbyzero.com
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| | | | | The study of cardinalities of infinite sets is one of the most intriguing areas of mathematics that an undergraduate mathematics major will encounter. It never fails to bring crooked smiles of joy, disbelief, confusion and wonder to their faces. The results are beautiful, deep, and unexpected. Recall that two sets have the same cardinality if... | |
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gowers.wordpress.com
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| | | It's been a while since I have written a post in the "somewhat philosophical" category, which is where I put questions like "How can one statement be stronger than an another, equivalent, statement?" This post is about a question that I've intended for a long time to sort out in my mind but have found... | ||
