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On 11/23/13 1:07 PM, Kreinovich, Vladik
wrote:
Do you mean instead of the above:We have gone through these questions when we started the standard. The range of a function over the interval is defined as the set of all possible values of the function when its arguments are in the range. If for some values within the range, the function is not defined, there are no values to add to the set. The range of a function over the interval is defined as the set of all possible values of the function when its arguments are in the function's domain of definition.
That is:
f(X) = { f(x) | x \in X \cap D_f };
where X is an interval and D_f is f's domain of definition.
Therefore, the interval extension of any function returns the empty set { } for any argument outside the function's domain of definition.
In this case, the containment set of 1 / [0, 0] is { }, the empty
set.Is this what you propose? If so, then I claim this is a containment failure because in the projective real system 1/0 = oo, which is not the empty set. Therefore there is an inconsistency in the proposed theory. Cheers, Bill |