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Concept

Interval

An interval is used to represent a set of values that lies between two numbers, or a set of values that are greater than or less than a specific number. Intervals are usually represented algebraically with inequalities and graphically with a number line. This is done by marking the endpoints of the interval and drawing a line segment between them.
Interval from 1 to 4

An interval consisting of real numbers contains an infinite amount of numbers. In the interval all numbers between and are part of the set. For example, and An interval does not have to be limited between two ends. For example, the inequality is the set of all positive real numbers greater than or equal to

Interval Notation

Interval notation is a way to denote an interval. In this notation, a square bracket, or is used when the end value is included, and a round bracket, or is used when the end value is not included. When using interval notation, the left value is less than the right value.

Interval Notation Description Type of Interval
Both ends are not included Open interval
Both ends are included Closed interval
or One end is not included Half-open interval
The following applet shows some more examples of intervals.
Examples of Intervals
Note that if the variable only has one limit, the other is infinity, or and is not included in the interval.
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