Misuse of Equal and Unequal to test equality of colors

Question

Start with:

    b = Blue; r = Red;

According to the docs, one should use Equal (==) and Unequal (!=) only for testing equality of such things as numeric objects and string objects; and one should use SameQ (===) and UnsameQ (=!=) otherwise.

So as expected, the following return unevaluated (except that the names of colors get replaced by color blobs):

    Red == Blue
    r == b
    Red != Blue
    r != b

Now, however, let:

    x = b;

Now all the below do evaluate to give True or False:

    x == Blue
(* True *)
    x == b
(* True *)
    x != Blue
(* False *)
    x != b
(* False *)

Why does Mathematica permit this?

Because any expression is Equal to itself and is not Unequal to itself. — Bob Hanlon, Apr 02 '20 at 20:16
@BobHanlon: But why does Red == Blue not evaluate completely to True or False? — murray, Apr 02 '20 at 20:50
(i) Things that are SameQ are also Equal. (ii) Things that are not NotSameQ are thus SameQ are thus Equal are thus not Unequal. — Daniel Lichtblau, Apr 03 '20 at 00:19

Somos · Answer 1 · 2020-04-02T22:28:14.530

1

The difference is that x=y assigns a value to x. So, if x does not have a value, it evaluates to itself. However try

ClearAll[x];
Print[x==x,":",x==0,":",x==Unevaluated[x]]

Now do x=0 and the Print statement again to see the difference. Note that I used 0 as just an example. Almost any Mathematica expression would do, but it is certain for atomic objects like integers and colors. Verify this for yourself.

edited Apr 02 '20 at 22:28

answered Apr 02 '20 at 21:45

Somos

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But your example sets x to be numeric. Please look again at my query! – murray Apr 02 '20 at 22:05

Misuse of Equal and Unequal to test equality of colors

1 Answers1