### Intervals in R

At the time of analyze the Real Number Set

**R**it is essential to associates subsets of

**R**with real numbers . This purpose is served by taking subsets of

**R**in a spacial way as follows .

**Open and Closed Intervals :-**An Open Interval of real number is a subset of

**R**defined as

**{x/ a<x<b}**i.e. it is the set of all real numbers that are greater then

**a**but less then

**b**. This open interval is denoted by

**(a ,b) or ]a, b[ .**

Thus ;

**(a, b) = {x/ a<x<b , x is element of R }**

and ;

**y is element of (a, b) => a<y<b .**

A closed interval of real number is subset of

**R**defined as

**{ x/ a is less then an equal to x is less then and equal to b }**

i.e. it is the set of all real numbers that are equal to or greater then

**a**but equal to or less then

**b**. This closed interval is denoted by

**[a , b] .**

Thus;

**[a, b]= {x/ a is less then and equal to x is less then and equal to b ,**

**where x is element of R}**

and

**y**is element of

**[a, b]=> a is less then and equal to y**

**and y is less then and equal to b .**

Clearly open and closed intervals are bounded sets in

**R**. While in case of

**(a, b)**there is no maximum or minimum element , in case of

**[a, b]**the maximum element is

**b**and the minimum element is

**a**.

Here is examples of open , closed ,semi open and semi closed intervals .

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