Interval Notation

What is Interval Notation

Definition

Interval Notation is a simplified notation for writing intervals using parentheses and brackets to show if the endpoints are included.

Example

Open interval does not include the endpoints. We show this with interval notation by using parentheses ( ) and graphing with open circles.

$\{x|x>5\}$

ex 1

$Set:$$\{x|x>5\}$ 

$(5,\infin)$

(5,\infin)

Interval Notation:  $(5, \infin)$

Graph:

ex 2

Set:  $\{x|-3<x<5\}$

$(-3,5)$(-3,5)

$Graph:$\{x|-3<x<5\}

ex 3

Set: $\{x|x<4\}$\{x|x<4\}

Interval Notation:  $(-\infin,4)$(-\infin,4)

Graph: 

Open and closed interval includes one endpoint and does not include the other.  We show this with interval notation by using parentheses for the open interval which does not include the endpoint and a bracket for the other which will include the endpoint.

ex 1

Set: $\{x|-4<x\le3\}$\{x|-4<x\le3\}

Interval Notation:  $(-4,3]$(-4,3]

Graph: 

Closed interval includes the endpoints.  We show this with interval notation by using square brackets [ ] and graphing it with closed circles.

ex 1

Set:  $\{x|-4\le x \le 3\}$\{x|-4\le x \le 3\}

Interval Notation: $[-4,3]$[-4,3]

Graph:

All real numbers have no endpoints.  We show this with interval notation by using parentheses ( ) and graphing with a line going to infinity.

ex 1

Set:  $\{x|x\,is\,a\,real\,number\}$\{x|x\,is\,a\,real\,number\}

Interval Notation:  $(-\infin,\infin)$(-\infin,\infin)

Graph:

By: Ed

Oct. 29, 2020