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homotopytypetheory.org | ||
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bartoszmilewski.com
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| | | | | This is part 13 of Categories for Programmers. Previously: Limits and Colimits. See the Table of Contents. Monoids are an important concept in both category theory and in programming. Categories correspond to strongly typed languages, monoids to untyped languages. That's because in a monoid you can compose any two arrows, just as in an untyped... | |
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xorshammer.com
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| | | | | In the book A=B, the authors point out that while the identity $latex \displaystyle{\sin^2(|10 + \pi x|) + \cos^2(|10 + \pi x|) = 1}$ is provable (by a very simple proof!), it's not possible to prove the truth or falsity of all such identities. This is because Daniel Richardson proved the following: Let $latex \mathcal{R}$... | |
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billwadge.com
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| | | | | The famous mathematician Kurt Gödel proved two "incompleteness" theorems. This is their story. By the 1930s logicians, especially Tarski, had figured out the semantics of predicate logic. Tarski described what exactly was an 'interpretation' and what it meant for a formula to be true in an interpretation. Briefly, an interpretation is a nonempty set (the... | |
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francisbach.com
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