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If $x$ is a positive rational number, then of course so is $2 x$.

How can we make Mathematica yield this result?

The obvious approach doesn't work:

Assuming[x \[Element] PositiveRationals,
 MemberQ[2 x, PositiveRationals]]

I've tried Reduce and so on, without success.

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1 Answer 1

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Assuming[Element[x, PositiveRationals], Simplify@Element[2*x, PositiveRationals]]

Mathematica graphics

Assuming[Element[x, PositiveRationals], Simplify@Element[Pi*x, PositiveRationals]]

Mathematica graphics

Help on Element says

enter image description here

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  • $\begingroup$ Oh gosh... that simple. Thanks. ($+1, \checkmark$) $\endgroup$
    – David G. Stork
    May 30 at 4:09

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