       Re: confused about == vs === in this equality

• To: mathgroup at smc.vnet.net
• Subject: [mg103761] Re: [mg103732] confused about == vs === in this equality
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Mon, 5 Oct 2009 07:38:26 -0400 (EDT)
• References: <20091003104738.LCJ3I.416659.imail@eastrmwml34> <200910040935.FAA07794@smc.vnet.net>

```I amy be taking a bit of a risk here, but I would guess that
ComplexInfinity and Indeterminate are the only symbols in Mathematica
with this property, that is we get:

a=ComplexInfinity

TrueQ[Unevaluated[x == x] /. x -> a]

False

a = Indeterminate;

TrueQ[Unevaluated[x == x] /. x -> a]

False

I believe that there are no other symbols for which this happens (?)
(If I am right and it is the only one that there is no need to be

Why does and Indeterminate and ComplexInfinity behave in this way? Of
course this is a matter of design and not (for example) mathematics so
the question really is, is this a reasonable and useful thing rather
than if it is right. I guess it is pretty clear that since
Indeterminate refers to a magnitude that cannot be determined, you
would not really want to assert that two expressions, both of which
evaluate to Indeterminate, are in any sense equal. For example it
would seem very strange if

Infinity - Infinity == Infinity/Infinity

returned True (as would have to be the case if
Indeterminate==Indeterminate returned True). Similar considerations
perhaps apply to ComplexInfinity, which refers to a complex quantity
with infinite magnitude but with an indeterminate argument. (However,
I am less convinced of that in the case of ComplexInfinty than in the
case of Indeterminate, because ComplexInfinity has a natural
interpretation as a unique point on the Riemann sphere).

(Of course === asks quite a different question and there is no doubt
that when you have identical expressions on both sides of === the

Andrzej Kozlowski

On 4 Oct 2009, at 18:35, Nasser Abbasi wrote:

> ?===
> lhs===rhs yields True if the expression lhs is identical to rhs, and
> yields
> False otherwise.
>
> ?==
> lhs==rhs returns True if lhs and rhs are identical.
>
> But looking at this example:
>
> a = ComplexInfinity;
> If[a == ComplexInfinity, Print["YES"]]
>
> Expecting it would print "YES", but it does not. it just returns the
> whole
> thing unevaluated? But
>
> If[a === ComplexInfinity, Print["YES"]]
>
> does return YES.
>
> I guess I am a little confused about the "expression" bit in the
> definition.
>
> So, when using the 3"=", it is looking at the _value_ of the
> expression, but
> when using the 2"=", it is looking at the expression _as it is_, i.e.
> without evaluating it?  Is this the difference?  I've always used
> the 2"="
> for equality, now I have to be more careful which to use.
>
> --Nasser
>
>
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```

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