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1. Between every two rational numbers are an infinite number of irrational numbers.

2.Between every two irrational numbers are an infinite number of rational numbers.

Quote2.Between every two irrational numbers are an infinite number of rational numbers.I don't see how this is consistent with (1). If you pick any two of the infinite set of irrational numbers "between" two "closest" rational numbers, then is this a counterexample?