# What is the Interval Notation and how do we Represent it?

The interval notation is the process of representing an interval on a number line. In this way it is a method of writing the subset of the real number line, an interval consisting of numbers lying between two specific numbers.

The Interval notation calculator makes it possible to draw an interval by satisfying the interval like 0 ≤ x ≤ 5. It is an interval containing all the numbers between 0 and 5 on the number line. The builder notation calculator is utilized to find the number line by giving the interval position on the number line.

Let us try to understand what is the interval and what are various forms of the interval.

The interval notation?

We know an interval expressed as 1 < x < 5 denotes a set of numbers lying between 1 and 5.

## Types of the intervals:

Intervals are classified and it is based on the numbers the set comprises of that interval.Some types of the interval do include the endpoints, and the other may not include the end point of the sets. Generally there are three types of intervals. The interval equivalent calculator can be used to find all the

• Open Interval
• Closed Interval
• Half-Open Interval

## Open Interval

This type of the interval has no end point, and it doesn’t have the sign of equal to any arm of the inequality. The Interval notation calculator solves the inequality with open intervals in a matter of seconds.

Consider the example of the , the open interval set {x | -6 < x < 2} and it does not include the endpoints, -6 and 2 in the interval and we have to write the number between the numbers. We can  express it using open interval notation: (-3, 1).

## Closed Interval

The closed interval also includes the endpoints of the inequality of the interval, when we write the inequality, then we also write the end points in our consideration. Consider the set the {x | -5 ≤ x ≤ 2}, it includes  the endpoints, – 5and 2.

It can be  expressed by using closed interval notation: [-5,2]. The Interval notation calculator includes the endpoints when we are writing the notation of a closed interval.

## Half-Open Interval

This type of interval includes only one of the endpoints of the inequality. For example, the set {x | -3 ≤ x < 1} include the endpoint -3. This is expressed using half-open interval notation: [-3,1)

## Symbol for Interval Notation

The notations we use for different intervals are:

• [ ]: This is a square bracket that is used when both the endpoints are included in the set.
• ( ): This is a round bracket that is used when both the endpoints are excluded in the set.
• ( ]: This is a semi-open bracket that is used when the left endpoint is excluded and the right endpoint is included in the set.
• [ ): This is also a semi-open bracket that is used when the left endpoint is included and the right endpoint is excluded in the set.

## Conclusion

The interval notation is a way of representing the subset of the real number on the number line. We can utilize this number line to represent the inequality on the number line, the  interval form calculator makes the graphical representation of the number line. The inequality like 1 < x < 6, it represents the number lying between 1 and 6.Make it possible to draw an interval line by the  Interval set notation calculator. You can draw a graph of the inequality on the number line by the interval notation graph calculator. Draw  the graph according to interval type and nature.