Interval

Symbols and graphs

Intervals may be written in various ways, depending on the characteristics of their endpoints a and b:

Consider a continuous set E of real numbers.

• An open interval of E with endpoints a and b is a subset of E written as (a, b) and consisting of all the elements of E strictly included between a and b. It is formally written as:
  (a, b) = {x ∈ E | \(a\) < x < \(b\)}.
  An open interval is graphically represented by a segment whose endpoints are open circles.

• A left half-open interval of E with endpoints a and b is a subset of E written as (a, b] and containing all the elements of E strictly greater than a and less than or equal to b. It is formally written as:
  (a, b] = {x ∈ E | \(a\) < x ≤ \(b\)}.
  A left half-open interval is graphically represented by a segment whose left endpoint is open and whose right endpoint is closed.

• A right half-open interval of E with endpoints a and b is a subset of E written as [a, b) and containing all the elements of E greater than or equal to a and strictly less than b. It is formally written as:
  [a, b) = {x ∈ E | \(a\) ≤ x < \(b\)}.
  A right half-open interval is graphically represented by a segment whose left endpoint is closed and whose right endpoint is open.

• A closed interval [A,B] of E is an interval whose endpoints are included. A closed interval is represented by a segment whose two endpoints are closed points. A closed interval is graphically represented by a segment whose two endpoints are closed.