Are you studying Limits and Continuity? Are you confused about the interval notation? Read on to know more about interval notation.

## What are intervals in calculus?

An interval is a range of values that are useful for the particular question at hand. For example, if one were to ask which numbers were less than 1 but greater than 0, we would need to answer with intervals. The answer is every number between 0 and 1 excluding both 0 and 1. However, this is a very long answer to write. In order to make things shorter and use a more mathematical representation, we use the interval notation. The answer to this particular question is (0,1).

## What are the brackets used in interval notation?

We have two brackets, namely rounded brackets ( ) and square brackets [ ].

Each of these brackets represents something different. Let us take the range of 0 to 1. We will now show each interval notation along with the meaning:

(0,1) : means all numbers between 0 and 1 excluding both 0 and 1

(0, 1]: means all numbers between 0 and 1 excluding 0 but including 1

[0, 1) : means all numbers between 0 and 1 including 0 but excluding 1

[0,1]: means all numbers between 0 and 1 including both 0 and 1

We often see these interval notations being used in problems related to limits and continuity. For example, if a function is continuous from -1 to 1 but is not defined at 0, we can write the domain as [-1,0) U (0, 1] where U is the union operator used in set theory.

**Important rule #1:**

Whenever we have infinity or -infinity as part of the range, we cannot use the square bracket as infinities are not definite and thus cannot really be included.

WRONG:

[ ∞ , a) , [ ∞ , a]

(a, ∞ ] , [a, ∞ ]

[- ∞, a) , [- ∞,a]

(a, – ∞] , [a, – ∞]

[ – ∞, ∞]

CORRECT

( ∞ , a) , ( ∞ , a]

(a, ∞) , [a, ∞)

(- ∞,a) , (- ∞,a]

(a, – ∞) , [a, – ∞)

(- ∞, ∞)

where a is any number.

**Important rule #2**

When writing any interval notation (a,b), (a,b], [a, b), [a,b], we must make sure that a

## Better preparation

Now that you are familiar with the interval notation, you can now work on as many limits and calculus problems as you like!

But what if you have doubts about certain topics and questions? After all, textbooks cannot explain every scenario. In order to help yourself get the most out of your books, consider taking up coaching. But wait, isn’t coaching expensive and time-consuming? Well, it needn’t be.

While traditional coaching IS expensive and exhausting for you to take up after a long day at school, online coaching isn’t. It is comparatively more affordable and allows you to walk at your own pace, at your own time. In order to get some expert advice, question papers, mock exams, and overall assistance join an online coaching platform. A popular one is Edureify.

Edureify provides a topic-wise set of questions that specific to the exam you choose to appear for. The platform also has an experienced set of teachers who specialise in each subject. You can request them to tutor you to improve your performance.

Edureify solving sets are designed in levels of increasing difficulty designed to test your preparation. In addition to this, be sure to participate in the game-quizzes and AIR challenges that are full of higher-order-thinking questions, mirroring exams like JEE. Edureify even allows you to test yourself based on various parameters: Concept Analysis, and Speed Analysis. Both are important to succeed in your boards exams and most entrances.

The recommendation is to get your Concept Analysis to a level you’re happy with, and then Speed Analysis- do not forget that many tests have negative marking, so strong concepts triumph over the speed of solving.

To learn more, visit www.edureify.com today!!