Show that these statements about the real number x are equivalent: (i) x is rational, (ii) x/2 is rational, (iii) 3x-1 is rational.

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- September 28th 2010, 07:34 AMlm6485Statements about the real number x
Show that these statements about the real number x are equivalent: (i) x is rational, (ii) x/2 is rational, (iii) 3x-1 is rational.

- September 28th 2010, 09:40 AMemakarov
Fill in ... in the following.

Recall the definition: x is rational if there exist integers m and n such that n > 0 and ...

Try proving (i) => (ii). Assume that x is rational. Then there exist m and n such that ... I need to show that x / 2 is rational. This means proving that there exist integers m' and n' such that x / 2 = ... Can I come up with such m' and n'?