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I have

e[m_, n_] := Sqrt[m - n]

How can I figure out, using Mathematica, for which m and n the statement is a Real number?

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    $\begingroup$ Assuming that $m$ and $n$ are real numbers themselves, Reduce[Sqrt[m - n] ∈ Reals, {m, n}, Reals]. Alternatively, get right of the Reals domain restriction in that command for a more general result. $\endgroup$ – MarcoB Nov 21 '16 at 16:56
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    $\begingroup$ With version 10 or later: FunctionDomain[Sqrt[m - n], {m, n}] $\endgroup$ – Bob Hanlon Nov 21 '16 at 17:28
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Here are two ways to do it.

MarcoB

Reduce[Sqrt[m - n] ∈ Reals, {m, n}, Reals]

n <= m

Bob Hanlon

FunctionDomain[Sqrt[m - n], {m, n}]

m - n >= 0

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