Consider the statement : Find the logical and/or computatio…
Consider the statement : Find the logical and/or computational error(s) in the following proof, if any. (1) Suppose not. That is, suppose that the sum of any two rational numbers is not rational. (2) This means that no matter what two rational numbers are chosen their sum is not rational. (3) Now both 1 and 2 are rational because and , and so both are ratios of integers with a non-zero denominator. (4) Thus, by supposition, the sum of 1 and 2, which is 3, is not rational. (5) But 3 is rational because , which is a ratio of integers with a non-zero denominator. (6) Hence, 3 is both rational and irrational, which is a contradiction. (7) This contradiction shows that the supposition is false, and hence is true.