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www.jeremykun.com | ||
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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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siddhartha-gadgil.github.io
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| | | | | [AI summary] The text discusses a formalization in Lean 4 of a mathematical result related to the group P and the unit conjecture. It outlines the construction of the group P as a metabelian group with a specific action and cocycle, the proof of its torsion freeness, and the use of decidable equality and enumeration to verify properties. The formalization also includes the construction of the group ring and the verification of Gardam's disproof of the unit conjecture by demonstrating the existence of a non-trivial unit in the group ring over the field F₂. | |
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almostsuremath.com
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| | | | | The aim of this post is to motivate the idea of representing probability spaces as states on a commutative algebra. We will consider how this abstract construction relates directly to classical probabilities. In the standard axiomatization of probability theory, due to Kolmogorov, the central construct is a probability space $latex {(\Omega,\mathcal F,{\mathbb P})}&fg=000000$. This consists... | |
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sreekar.ch
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| | | But first What is functional programming ? Functional programming is a programming paradigm in which most computation is treated as evaluation of functions. It emphasizes on expression evaluation instead of command execution. Wikipedia When did it all start ? In the 90s, there was a war between declarative programming and imperative programming. Declarative programming then represented by logic programming languages like Prolog and early functional languages like Erlang. And imperative languages were r... | ||
