it's worth mentioning the infinite number of decimal places isn't an issue. there is the formalism of computable numbers to get around this https://en.wikipedi

it's worth mentioning the infinite number of decimal places isn't an issue. there is the formalism of computable numbers to get around this https://en.wikipedia.org/wiki/Computable_number https://en.wikipedia.org/wiki/Computable_number roughly represent each number as a turing machine, which on input i outputs the ith digit. it works fine (it's slower than floats, but that's a different concern). the issue is that the computable numbers are relatively small. in particular, there are countably many turing machines, so they're a countable subset (in fact subfield) of the reals. so in a precise sense they only make up a vanishingly small fraction of the real numbers. but they still capture many important mathematical constants, e.g. e and pi.