# Answer to Question #20314 in Discrete Mathematics for paige williams

Question #20314

Prove by Contradiction: there is no smallest positive rational number

Expert's answer

Suppose there is a smallest positive rational number. Now divide it by 2. That is still a positive rational number but is only half as big. Contradiction. Therefore the assumption that there is a smallest positive rational number cannot be true. Hence there is no smallest positive rational number.

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