A (real) interval is a set of real numbers between two other numbers. Intervals of are commonly used in graphs. An open interval excludes the end points, while the end points of a closed interval are elements. Some intervals may partially open and closed. 

An (integer) interval is basically the same as a real interval, except it consists of integers.

Formal definitions

Real interval

  • Open interval:
  • Closed interval:
  • Left open, right closed:
  • Right closed, right open:

Integer interval

  • Open interval:
  • Closed interval:
  • Left open, right closed:
  • Right closed, right open:

Arbitrary partially ordered set

Let be a poset.

Let be the irreflexive kernel of

Then, an interval may be defined as:

  • Open interval:
  • Closed interval:
  • Left open, right closed:
  • Right closed, right open:
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