In the study of Mathematics, interval Notation means to present the interval which is provided on a typical number line. This interval notation is used to write the subsets of the real number line on it. The interval notation has numbers that lie between other specific numbers. 

Like, the set of numbers ‘Y’ satisfies this set which goes like 0 ≤ x ≤ 6, this illustrates that the interval consists of numbers that range between 0 to 6, while this means all the numbers from 0 to 6 will be present here in the set.

Expression of Interval Notation  

With the help of Interval Notation (more info), we can express the subset of the real numbers which is present in the number system. This notation can be used to represent the inequalities that are there between the sets. Like in the above-given example, the sets represent the numbers that are lying between 0 to 6. 

Give Some Examples of Interval Notation 

In an example that is to be taken, we want to express the numbers which are present between 8 and 19, so we can express this in the form of Interval Notation – Interval Notation (8,19).

What Are the Types of Intervals?

The interval types can be classified on the basis of the numbers which is present in the set. In these types of sets, there can be endpoints, while in some other sets endpoints may not be available. Thus, to classify, generally, there are three types of intervals, these are as follows:

  1. Open Interval
  2. Closed Interval
  3. Half-Open Interval

Here we see that there are three types of Intervals. All these types of Intervals are based on different sets of numbers and their usages. 

Now, we will explain the different types of Intervals. 

What is Open Interval? 

Open Interval, are those intervals that do not include the endpoints of the inequality. Like, the set {x | -6 < x < 1} have no endpoints. This type of interval is thus expressed as open interval notation: (-6,1)

What is Closed Interval?

Closed Interval includes the endpoints of the inequality. Like the set {x | -8 ≤ x ≤ 1} have the endpoints, and thus this can be expressed as using the closed interval notation – [-8,1]

What is Half-Open Interval?

Half-Open type Interval only has one endpoint which is of inequality. Like the set {x | -7 ≤ x < 1} includes the endpoint -7. This is being represented by utilizing the half-open interval notation – [-7,1]. 

Presentation of Symbols for Interval Notation

The notations which are used for the different types of intervals are as follows: 

  • [ ]: This square bracket is being used to represent that both the endpoints are being included in the set. 
  • ( ): The round brackets are used to identify that both the endpoints are excluded from the set. 
  • ( ]: This is the semi-open bracket type that is used when the left-endpoint is being excluded while the right endpoint is being included in the set. 
  • [ ): This is too a semi-open bracket which represents that the left endpoint is included and the right endpoint is excluded from the set. 

Lesson Round-up for Interval Notation

These are the following notes, which are to be borne in mind. The students are requested to go through these notes so that they can solve the problems which are based on Interval Notation with high calibre. Following are the things to remember: 

  • Interval Notation is the expression of Inequalities. 
  • Three types of notations. 
  • No infinity symbol – Bounded interval
  • Infinity symbol present – Unbounded Interval. 

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