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Set theory proof

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Undergraduate senior level Real Analysis.
Please show me formal math proofs.

Show that Q(set of rational numbers) ~ N(set of natural numbers).

(Suggestion from my professor: prove by letting set Qn < Q and a/b (a and b are some integers, but b is not zero) and Q = union of Qn (Qn = Q1, Q2, Q3, ....) .)

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This provides an example of a proof regarding rational and natural numbers.

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