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 …
Ratios are numbers, too. Rational numbers are ratios between integers, and they can be fully known. While Pi is the ratio between circumference and diameter of a circle, it is not a rational number. You cannot calculate all of Pi.
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What do you like as a definition of "number"?
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informally, it is a subsequent labeling scheme
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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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