Re: 1/[0,2]=NaI
Nate Hayes wrote:
Arnold Neumaier wrote:
Nate Hayes wrote
(in: Re-submission of motion 5: multiple-format arithmetic):
Arnold Neumaier wrote:
Nate Hayes schrieb:
Arnold Neumaier wrote:
Nate Hayes schrieb:
.
.
.
My position on this subject therefore allows you to compute
1/[0,2]=[1/2,Inf) in your range enclosure example, i.e., it allows to avoid
NaI in this case because it implies
1/[0,2] = 1/[0,0] \union 1/(0,2]
= {empty} \union [1/2,Inf)
= [1/2,Inf)
According to my understanding, THE ABOVE (taking the union of limiting
of point values) is the basic idea underlying csets, for what it's worth.
In the context of predicate logic, though, such an interpretation is not
correct. For example, if I seek values of y such that
(for all x \in [0,2]) y = 1/x
is true, there is no value of y when x=0 to make the conditional equation
true.
But doesn't classical interval arithmetic (which I thought is the basic
thing we are standardizing) seek
(the set of all y such that there exists an x \in [0,2] with y=1/x) ??
That is different from what you have above.
So the predicate is undefined, i.e., NaI (this is why in Moore's
classical arithmetic division by zero is undefined).
Huh?
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