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!
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