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Let the cardinal number of N, the set of all natural numbers, be א0. Prove that...

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Basic Math

Let the cardinal number of N, the set of all natural numbers, beא0. Prove that the product set N × N = {(m,n);m ∈ N,n ∈ N} has thesame cardinal number. Further prove that Q+, the set of allpositive rational numbers, has the cardinal number N_0.

Hint: You may use the formula 2^(m−1)(2n − 1) to define afunction from N × N to N, see the third example on page 214 of thetextbook.

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