Mathematicians may be undecided about whether they live in a universe where the continuum hypothesis holds, but machine learning lives in a universe of countable numbershttps://www.nature.com/articles/d41586-019-00083-3 …
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The vast majority of “Real”
numbers are not computable. Unlike pi and e, which are computable, most Reals can’t be specified in a finite way. They can’t be chosen or generated algorithmically (hence Axiom of Choice needed).
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Pascal's triangle can indeed generate ALL (positive) real numbers, can't it? (All possible patterns are calculated, eventually (it's an infinite function).)
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Is it possible that our mind “is created” by “uncountable values” to operate with “concrete” functions...?
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I thought what you have to take home from Gödel's findings is: Give up trying to create a global axiomatic theory because there will always be true statements unprovable in your theory. Assuming "there are only integer values": which true statements are you unable to prove then?
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