Derek Martin wrote:
On Fri, Jan 02, 2009 at 12:50:44PM -0800, Erik Max Francis wrote:
Identity isn't defined on math objects, only on Python objects; there
is no notion of 'is' in math.
This is also false, it even has its own operator (which requires
Unicode to display): ≡
That can mean a number of things, one of which means "is identically
equal to,"
Quite so.
but identity means something different in mathematics than it means
here.
But for non-mutable objects, aren't they essentially the same?
Mathematics has no concept of "objects" in the sense that computer
science does, so of course the best you can really do is draw
parallels.
That's exactly the point. There is no concept of object identity in
mathematics, so the above statement that you called false is, in fact,
true. The concept does not translate.
In computer science, identity means that two expressions are
represented by the same object, something which not only has no
meaning in mathematics,
We're getting way off track here, but I would argue this is also
false. Take sets, for example:
A = { 1, 2, 3 }
B = { 1, 2, 3 }
Is it not true that A ≡ B and in fact these two sets are the same,
i.e. they are not actually two different sets at all; the have the
same identity, even considering a definition of "identity" which
reflects that in Python?
Only if you try to make up a concept of identity that mathematics
doesn't already have. The existing concept, which you invoked, has
nothing to do with _object_ identity, it just has to do with a broader
equality.
I don't imagine I would agree, based on what I just said. To elaborate,
each side of the expression contain symbols which always evaluate to
the same constant. The identity of a constant is constant. :)
Except identities don't have to contain constants at all. They can
contain arbitrary expressions on either side of the "is identically
equal to" symbol. Which clearly indicates that the symbol can't mean
the same thing as the identity operator in computer science, as you were
claiming it did.
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