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As the title of the question suggest. Is there any tool that generalizes all mathematical operations, like adding, subtracting, dividing or even integrating, deriving or making a matrix transformation. The most accurate example that I can think of now is the generalized Stoke's Theorem or in a similar way that of a Physicist that makes a model to explain many phenomena of nature.

I don't know if this question sounds pedantic and little scientific, but I would like to know it, just for divulgative propose.

Martin Argerami
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Álvaro Rodrigo
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  • I'm not so familiar, but apparently there were a lot of algorithms to do almost anything with a slide rule back in the day, frequently reducing multiplication of large numbers to addition of associated logarithms, then back again. It was a very versatile tool set. Could be worth looking into. – TurlocTheRed Feb 07 '22 at 16:28
  • The problem with continued generalization for its own sake is that the more general the framework, the less it says about any specific case, and in the limit you wind up saying nothing about everything. (Surely something like this must be a famous quote by someone, but it pretty much fell out for me as I was writing this comment -- moments later google search.) – Dave L. Renfro Feb 07 '22 at 21:24

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Think about set-theoretic (crisp) operations. Zadeh's extension principle extends these operations to fuzzy sets.

Wuestenfux
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