sup and inf

[mvolkmann]

I'm trying to learn about sup and inf. I tried to find good documentation on this, but came up empty.
Do these represent the maximum supported integer value or positive infinity?
What is the difference between sup and inf?
Can inf/0 only be used as the lower bound of a range using the .. operator?
Can sup/0 only be used as the upper bound of a range using the .. operator?
Are these defined by CLP libraries or considered a builtins?

[mvolkmann]

Based on this Wikipedia page: https://en.wikipedia.org/wiki/Infimum_and_supremum
the following seems like a reasonable answer:

In the domain of integers:

• The atom inf represents the greatest value
  that is less than or equal to all integers.
  This can be thought of as negative infinity.
• The atom sup represents the least value
  that is greater than or equal to all integers.
  This can be thought of as positive infinity.

Can someone confirm this?

[mvolkmann]

Is it correct to say that inf represents negative infinity and can only be used as the lower bound of a range?
And is it correct to say that sup represents positive infinity and can only be used as the upper bound of a range?

[UWN]

The notion of positive and negative infinity is even more problematic. Even more so as in some number systems they are provided as (continuation) values that can be used for some calculations.

[mvolkmann]

Can you give me an example of such a number system?

[UWN]

IEEE 754

[mvolkmann]

I want to mark this question as answered, but I feel like we still haven't found an agreed upon way to describe sup and inf and I haven't found good descriptions on the web.

For example, suppose we are using either the integer or real number system. Would you say that sup is the upper bound of that number system, but is somehow different from positive infinity?