Return to Answer

I think a solution based on pattern matching will be much faster than ones based on Element (which is more mathematical in usage) or pattern tests or anythign else that forces evaluation, since we can bypass the main evaluator.

ClearAll@realQ
SetAttributes[realQ, Listable]
realQ[_Real | _Integer | _Rational] := True

realQ[Catalan | ChampernowneNumber | Degree | E | EulerGamma | Internal`Euler2Gamma |
      Glaisher | GoldenRatio | Khinchin | MachinePrecision | Pi] := True

realQ[Complex[_, 0.]] := True
realQ[_] := False

realQ[{"text", 0, 3.0, 1/2, I, Pi, 1 + 0. I}]
(* {False, True, True, True, False, True, True} *)

The list in the second definition was obtained using

Select[Names["*`*"], MemberQ[Attributes@#, Constant] &]

I think a solution based on pattern matching will be much faster than using Element (which is more mathematical in nature) or only pattern tests or anything else that forces evaluation, since we can bypass the main evaluator. However, it is not possible to completely escape evaluation, because there can be infinitely large number of possibilities for a real number that cannot be matched solely by pattern matching. Hence, the following tries to delegate as much as possible to the pattern matcher and evaluates only what's necessary. The unfortunate consequence is that it is no longer immune to prank entries such as Unevaluated@Pause@10.

ClearAll@realQ
SetAttributes[realQ, Listable]
realQ[_Real | _Integer | _Rational] := True

realQ[Catalan | ChampernowneNumber | Degree | E | EulerGamma | Internal`Euler2Gamma |
      Glaisher | GoldenRatio | Khinchin | MachinePrecision | Pi] := True

realQ[Complex[_, 0.]] := True
realQ[x_] := NumericQ[x]

realQ[{"text", 0, 3.0, 1/2, I, Pi, 1 + 0. I}]
(* {False, True, True, True, False, True, True} *)

The list in the second definition was obtained using

Select[Names["*`*"], MemberQ[Attributes@#, Constant] &]

I think a solution based on pattern matching will be much faster than ones based on Element (which is more mathematical in usage) or pattern tests or anythign else that forces evaluation, since we can bypass the main evaluator.

ClearAll@realQ
SetAttributes[realQ, Listable]
realQ[_Real | _Integer | _Rational] := True
realQ[_Symbol?NumericQ] := True
realQ[Complex[_, 0.]] := True
realQ[_] := False

realQ[{"text", 0, 3.0, 1/2, I}]
(* {False, True, True, True, False} *)

I think a solution based on pattern matching will be much faster than ones based on Element (which is more mathematical in usage) or pattern tests or anythign else that forces evaluation, since we can bypass the main evaluator.

ClearAll@realQ
SetAttributes[realQ, Listable]
realQ[_Real | _Integer | _Rational] := True

realQ[Catalan | ChampernowneNumber | Degree | E | EulerGamma | Internal`Euler2Gamma |
      Glaisher | GoldenRatio | Khinchin | MachinePrecision | Pi] := True 

realQ[Complex[_, 0.]] := True
realQ[_] := False

realQ[{"text", 0, 3.0, 1/2, I, Pi, 1 + 0. I}]
(* {False, True, True, True, False, True, True} *)

The list in the second definition was obtained using

Select[Names["*`*"], MemberQ[Attributes@#, Constant] &]

I think a solution based on pattern matching will be much faster than ones based on Element (which is more mathematical in usage) or pattern tests or anythign else that forces evaluation, since we can bypass the main evaluator.

ClearAll@realQ
SetAttributes[realQ, Listable]
realQ[_Real | _Integer | _Rational] := True
realQ[_] := False

realQ[{"text", 0, 3.0, 1/2, I}]
(* {False, True, True, True, False} *)

I think a solution based on pattern matching will be much faster than ones based on Element (which is more mathematical in usage) or pattern tests or anythign else that forces evaluation, since we can bypass the main evaluator.

ClearAll@realQ
SetAttributes[realQ, Listable]
realQ[_Real | _Integer | _Rational] := True
realQ[_Symbol?NumericQ] := True
realQ[Complex[_, 0.]] := True
realQ[_] := False

realQ[{"text", 0, 3.0, 1/2, I}]
(* {False, True, True, True, False} *)