An IntegerRegion can be thought of as the disjoint union of intervals and inequalities.

The interesting cases to look at are:

The distinctions:

1) The empty region

2) The full region

3) A "left" inequality -- e.g., everything less that 3.

4) A "right" inequality -- e.g., everything greater than or equal to 7

The non-distinction simple regions:

5) An interval -- e.g., from 3 inclusive to 7 exclusive

The non-simple regions:

6) A disjoint union of (in order) an optional left inequality, a set of intervals, and an optional right inequality.

If a non-empty region has a least element, then it "isBoundedLeft". Otherwise it extends leftwards indefinitely. Similarly, if a non-empty region has a greatest element, then it "isBoundedRight". Otherwise it extends rightwards indefinitely. (We may figuratively speak of the region extending towards + or - infinity, but we have purposely avoided introducing any value which represents an infinity.)

Looking at cases again:

1) "isBoundedLeft" and "isBoundedRight" since it doesn''t extent indenfinitely in either direction. (A danger to watch out for is that this still has niether a greatest nor a least element).

2) neither.

3) "isBoundedRight"

4) "isBoundedLeft"

5) "isBoundedLeft" and "isBoundedRight"

6) "isBoundedLeft" iff doesnt include a left inequality, "isBoundedRight" iff doesnt include a right inequality.

An efficiency note: Currently many of the method which could be doing an O(log) binary search (such as hasMember) are instead doing a linear search. This will be fixed if it turns out to be a problem in practice.