So from what I've been reading rational numbers are a countable infinity, while the irrationals are an uncountable infinity. So the number of irrational numbers > the number of rational numbers. Irrational numbers can "normal irrationals" or transcendental numbers, or at least that is what I've read. This seems pretty intuitive, a random number would more likely be irrational than rational.(adsbygoogle = window.adsbygoogle || []).push({});

So I was thinking, given a infinite random number generator would a given real be more likely to be represented as either a rational number or as a root of polynomial than transcendental? Or is this comparison impossible since I'd guess that transcendental numbers being a subset of an uncountable infinity are also an uncountable infinity? Or is this not true?

Any information would be great, or where to start reading about set theory.

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# B Real Probability

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