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Re: A Level 2 query - X-X / you only

This is a philosophical question about identity of numbers.

Are 2 numbers the same if they occur in the same memory location?
Are 2 numbers different if they occur in different memory locations, perhaps even in different computers? 

For some systems  expressions are "hashed".
In them, it is impossible to have 2 numbers with the same value that are stored in different locations. 
Bad news for intervals.
I will try to formulate a more thoughtful response to this next week, though I think we did some of it previously. 


On 7/3/2013 12:46 PM, Ralph Baker Kearfott wrote:

I would say that, in any case, it be important for the
programmer to know what the compiler is doing, for
mathematically rigorous computations.  Are there cases
that we haven't foreseen?

Baker

On 07/03/2013 01:36 PM, Kreinovich, Vladik wrote:

This may be not OK, if we have two different values X and Y for which it
so happens that their bounds coincide, so instead of saying Y =
[5.0,10.0], a programmer may want to save time and write Y  = X, but
these are still different quantities about which we cannot assume that
the actual values are equal

I think it is safe to optimize X-X to 0, but NOT the other two examples

*From:*stds-1788@xxxxxxxx [mailto:stds-1788@xxxxxxxx] *On Behalf Of *Ian
McIntosh
*Sent:* Wednesday, July 03, 2013 12:19 PM
*To:* stds-1788@xxxxxxxxxxxxxxxxx
*Subject:* Re: A Level 2 query - X-X

For intervals it would be OK to do the same for
SUB = X - X;
(except for infinite bounds) because X is identical to X, and for
X = [5., 10.];
Y = X;
Z = X - Y;
because the value Y represents is identical to X and none of the bounds
is infinite, and for
U = [5., 10.];
X = U;
Y = U;
Z = X - Y;
because X and Y are always identical,