[Question][Hw4] About Infinite in interval domain

[yongwoo36]

Hello professor.
I have a question about interval domain in HW4.

While doing my homework, I came to think about the result of add [MInf, MInf] [PInf, PInf].
I can't find the definition of the result of MInf + PInf.

But first, I wondered if an interval like [MInf, MInf] or [PInf, PInf] could exist, and I thought it couldn't.
The reason is, for example, if my understanding is correct, the result of [MInf, PInf] < [MInf, 10] is [MInf, 10], not [MInf, MInf].

Therefore, as in the first example, there is no case where PInf comes on the left side of interval or MInf comes on the right side of the interval, so I thought that we do not have to consider these cases.

Am I correct? Or is there something I misunderstood?
If so, what is the result of add [MInf, MInf] [PInf, PInf]?

Thank you.

[hyunsukimsokcho]

MInf (or PInf) is not a value to be rigorous, instead it is used to indicate any negative (or positive) value is included in the specified interval. Thus, both [MInf, MInf] and [PInf, PInf] are invalid interval. You really don’t need to consider them as operands when defining abstract operators.

[yongwoo36]

Thanks!

[ShinWonho]

Hello, I also have a question about infinite.

Can I assume PInf as finitely big number?? (Similarly MInf as finitely small number)
Why I ask this question is that PInf * 0 is not defined.
In our homework, mul [2, PInf] [0, 0] can be the case.
Can I assume mul [2, PInf] [0,0] is [0,0]?

Thank you

[KihongHeo]

Yes. Here Pinf and Minf do not exactly mean the ones in (rigorous) math. They are just symbols representing "arbitrary large (or small)" numbers.

[ShinWonho]

Thank you professor!!