Eroxl's Notes
Interval

An interval is a subset of all read numbers between two points.

There are three types of intervals

  1. Open Interval - An interval that does not include both it's endpoints
  2. Closed Interval - An interval that includes both it's endpoints
  3. Half-Open Interval - An interval that only includes one of it's endpoints
Note

Infinity can not be included in the endpoints of an interval so any interval including infinity is either a open interval or a half-open interval

Notation

Interval Notation

Open Intervals

Open intervals are denoted using parentheses ("") for example an open interval between and would be denoted using .

Closed Intervals

Closed intervals are denoted using square brackets ("") for example a closed interval between and would be denoted using .

Half-Open Intervals

Half-open intervals are denoted by a mix of square brackets ("") and parentheses (""). The endpoint that is included is denoted by a square bracket and the endpoint that is not included is denoted with a parenthesis. For example an half-open interval between and that includes but not would be denoted by . Alternatively if it included but not it would be denoted as .