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almostsuremath.com | ||
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xorshammer.com
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| | | | | There is a class of all cardinalities $latex \mathbf{Card}$, and it has elements $latex 0$, $latex 1$ and operations $latex +$, $latex \cdot$, and so forth defined on it. Furthermore, there is a map $latex \mathrm{card}\colon\mathbf{Set}\to\mathbf{Card}$ which takes sets to cardinalities such that $latex \mathrm{card}(A\times B)=\mathrm{card}(A)\cdot\mathrm{card}(B)$ (and so on). Ordinary generating functions can be thought... | |
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www.randomservices.org
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xorshammer.com
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| | | | | There are a number of applications of logic to ordinary mathematics, with the most coming from (I believe) model theory. One of the easiest and most striking that I know is called Ax's Theorem. Ax's Theorem: For all polynomial functions $latex f\colon \mathbb{C}^n\to \mathbb{C}^n$, if $latex f$ is injective, then $latex f$ is surjective. Very... | |
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donsbot.com
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| | | SMT solvers are automated tools to solve the "Satisfiability Modulo Theories" problem -- that is, determining whether a given logical formula can be satisfied. However, unlike SAT solvers, SMT solvers generalize to solving such NP-complete problems that contain not just boolean variables, but more useful types, such as lists, tuples, arrays, integers and reals. And... | ||
