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Re: A proposal for motion 5 "Arithmetic operations for intervals"

John Pryce wrote:
> 3. I suggest in the unlabeled eqn on p4, you replace
>        aa ◦ bb := { a ◦ b | a in aa and b in bb }
>     by
>        aa ◦ bb := { a ◦ b | a in aa and b in bb and a o b is
> defined }
>     to make it quite clear that out-of-domain points are just ignored
> in this definition.

I believe both definitions are required: the former agrees with the logic of
modal intervals and the latter agrees with the logic of c-sets.

For addition, subtraction and multiplication, the distinction is trivial.
But for division, it leads to two complementary operations:

    op1:    1/[-2,3] = (-Inf,-1/2] \union NaI \union [1/3,+Inf) = NaI
    op2:    1/[-2,3] = (-Inf,-1/2] \union {empty} \union [1/3,+Inf) =
(-Inf,-1/2] \union [1/3,+Inf)

I do not object that 1788 includes definitions for c-sets, but I object if
it is the *only* definition provided.

Nate