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micromath.wordpress.com | ||
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educationechochamber.wordpress.com
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| | | | | There are few simple solutions in education. If you are being promised one, it is at best a hopeful fib, at worst a deceptive sales-pitch. But there are some helpful principles that can guide our actions. A useful one I think could help improve literacy in primary and secondary schools: write less; read more. It... | |
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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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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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unstableontology.com
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| | | (note: one may find the embedded LaTeX more readable on LessWrong) The Löwenheim-Skolem theorem implies, among other things, that any first-order theory whose symbols are countable, and which has an infinite model, has a countably infinite model. This means that, in attempting to refer to uncountably infinite structures (such as in set theory), one "may... | ||
