I have some comments and I am sure Bill will elaborate and/or correct me if I am wrong.
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I do understand, and always have understood, that there are inequalities in things that are infinite. The set of numbers from 0 to infinity would be greater than the set of even numbers from 0 to infinity which in turn is greater than the set of prime numbers from 0 to infinity, and so on. All are infinite but some are larger than others.
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Since your examples are all denumerable sets, they are all the same size sets.
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What I do not understand here is why "denumerable" describes the term "0.999...999", where the "9's" are endless, but "infinite" does not.
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Assuming that you meant .999... with no terminal value, that set is both infinite and denumerable.
---Al
