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?

  • 4
    $\begingroup$ 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
    Commented Nov 21, 2016 at 16:56
  • 4
    $\begingroup$ With version 10 or later: FunctionDomain[Sqrt[m - n], {m, n}] $\endgroup$
    – Bob Hanlon
    Commented Nov 21, 2016 at 17:28

1 Answer 1


Here are two ways to do it.


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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