Which adjective describes the "either ... or ..." relationship? [duplicate]

Solution 1:

In mathematical literature, "complete" is the usual term, e.g.

...completeness implies that there are not any “gaps” (in Dedekind's terminology) or “missing points” in the real number line... https://en.wikipedia.org/wiki/Completeness_of_the_real_numbers

The Completeness of the Integers, John McCuan, February 25, 2020 https://people.math.gatech.edu/~mccuan/courses/4317/integers2.pdf

Picking up on the comment by @271828, I would say that "exhaustive" is equally correct in general speech. It doesn't even depend on there being merely two alternatives.

E.g. The digits 0-9 are exhaustive when it comes to expressing the numbers from zero to one hundred.

In other words they exhaust the possibilities. In less formal terms, you could say "all encompassing", however your example is mathematical and so formal by definition.

EDIT

Incidentally, the terms necessary and sufficient are relevant here. For example Even and Odd numbers are sufficient to encompass the integers but they aren't necessary, i.e. you can describe integers in a different way.