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thehousecarpenter.wordpress.com | ||
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xorshammer.com
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| | | | | We think of a proof as being non-constructive if it proves "There exists an $latex x$ such that $latex P(x)$ without ever actually exhibiting such an $latex x$. If you want to form a system of mathematics where all proofs are constructive, one thing you can do is remove the principle of proof by contradiction:... | |
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inquiryintoinquiry.com
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| | | | | Introduction The praeclarum theorema, or splendid theorem, is a theorem of propositional calculus noted and named by G.W.Leibniz, who stated and proved it in the following manner. If a is b and d is c, then ad will be bc. This is a fine theorem, which is proved in this way: a is b, therefore... | |
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mikespivey.wordpress.com
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| | | | | Equations of the form $latex x^3 = y^2 + k$ are called Mordell equations. In this post we're going to prove that the equation $latex x^3 = y^2 -7$ has no integer solutions, using (with one exception) nothing more complicated than congruences. Theorem: There are no integer solutions to the equation $latex x^3 = y^2... | |
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nicholasjoncrane.wordpress.com
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| | | There are a number of stimulating reflections/provocations/proposals, etc., in this post by John Krygier about Matt Wilson'sNew Lines. | ||
