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nickdrozd.github.io | ||
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eklausmeier.goip.de
[AI summary] This article explains the mathematical method of diagonalization, using Cantor's proof of uncountability and Turing's halting problem as primary examples. |
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jdh.hamkins.org
I'd like to share a simple proof I've discovered recently of a surprising fact: there is a universal algorithm, capable of computing any given function! Wait, what? What on earth do I ... |
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xorshammer.com
There are many functions from $latex \mathbb{N}$ to $latex \mathbb{N}$ that cannot be computed by any algorithm or computer program. For example, a famous one is the halting problem, defined by $latex f(n) = 0$ if the $latex n$th Turing machine halts and $latex f(n) = 1$ if the $latex n$th Turing machine does not... |
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www.jeremykun.com
Last time we worked through some basic examples of universal properties, specifically singling out quotients, products, and coproducts. There are many many more universal properties that we will mention as we encounter them, but there is one crucial topic in category theory that we have only hinted at: functoriality. As we've repeatedly stressed, the meat of category theory is in the morphisms. One natural question one might ask is, what notion of morphism is there between categories themselves? |
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