Re: A proposal for the next motion
On 2009-05-22 11:42:10 -0400, Nate Hayes wrote:
> In the world of intervals, it is misguided to call it a "trick." An example
> was already given in discussions in the ER subgroup, but I will re-present
> it here for those who have not seen:
>
> Given the conditional equation
>
> (x^2-1)/(x-1) = x+1
>
> over domain [-4,4], what is the mathematical *truth* of the situation?
> Clearly the equation is false, because the expressions on left and right
> side are not equivalent, i.e., they are not equal when x = 1. However,
> c-sets say the two expressions are equivalent, because use of {empty} in the
> left side of the equation produces same result as the right side.
I don't know what c-sets define exactly, but no, the expressions
(x^2-1)/(x-1) and x+1 are not mathematically equivalent, because
the left one isn't mathmetically defined at the point x = 1.
But interval arithmetic cannot even consider mathematical equivalence,
because of the rounding.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.org/>
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Work: CR INRIA - computer arithmetic / Arenaire project (LIP, ENS-Lyon)