Mathematics, 21.10.2020 16:01 williams5847
rove the following statement directly from the definition of rational number. The difference of any two rational numbers is a rational number. Proof: Suppose r and s are any two rational numbers. By definition of rational, r = a b and s = c d for some ---Select--- a, b, c, and d with ---Select--- . Write r β s in terms of a, b, c, and d as a quotient of two integers whose numerator and denominator are simplified as much as possible. The result is the following. r β s = Both the numerator and the denominator are integers because ---Select--- . In addition, bd β 0 by the ---Select--- . Hence r β s is a ---Select--- of two integers with a nonzero denominator, and so by definition of rational, r β s is rational.
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rove the following statement directly from the definition of rational number. The difference of any...
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