# What is Interval Notation?

In mathematics, a number line can be defined as the representation of numbers on a line that is straight. The method or process of expressing the intervals on these lines which are called number lines is known as the interval notation. We can also define interval notation as the representation of subsets on straight lines. The literal meaning of the term ‘literal’ is the numbers that lie between two different given numbers. Mathematically, it is represented as the number 1 which is smaller than ‘x’< then 5, this is basically the number that lies between 1 and 5. In this article, we will try to cover some topics related to interval notation such as the different types of intervals, symbols used for the notations, and detailed analysis about them.

## Various Different Types of Intervals

As mentioned above, intervals are the number lying between two different numbers. The intervals have been classified into various different types on the basis of the numbers its set is composed of. Basically, there are three types of intervals that are given. The following points analyses the types of intervals.

• A type of interval which is not inclusive of the inequality of endpoints is defined as the open interval. Let us take an example, the set of -3 smaller to x < 1 is not inclusive of the initial and terminal points, 1 and 3. The interval notation used to express this type of example is, : (-3, 1).
• A type of interval which is exactly opposite to that of the open interval is regarded as the closed interval. It is inclusive of the inequality of endpoints.  Let us take an example, the set of -3 smaller to x < 1 is inclusive of the initial and terminal points, 1 and 3. The interval notation used to express this type of example is, [-3, 1].
• A type of interval which is inclusive of only one endpoint is defined as the half-open interval.  Let us take an example, the set of -3 smaller to x < 1 is inclusive of only one point that is 3. The interval notation used to express this type of example is, (-3, 1).

## Different Types of Symbols used for Interval Notation

As mentioned above, there are different types of intervals. Likewise, there are various types of interval notation as well. The following points analyses those symbols.

• The symbol used when both the points at the end are included is given by, [ ):. It is also known as the square of brackets.
• The symbol used when both the points at the end are excluded is given by, ( ). It is also known as the round bracket.
• Whenever the endpoint of the right side is included and the endpoint of the left side is excluded, the following symbol is used, ( ]:. It is also known as the semi-open bracket.
• Whenever the endpoint of the right side is excluded and the endpoint of the left side is included, the following symbol is used, [ ):.

If you want to learn more about interval notation, in a detailed manner, in a fun way, and in an interactive manner, visit the Cuemath website.

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