# JEE Main & Advanced Mathematics Functions Intervals

## Intervals

Category : JEE Main & Advanced

There are four types of interval:

(1) Open interval : Let a and b be two real numbers such that $a<b$, then the set of all real numbers lying strictly between $a$ and $b$ is called an open interval and is denoted by $[a,\,\,b]$ or $(a,\,\,b)$. Thus, $[a,\,\,b]$ or  $(a,\,\,b)=\{x\in R\,:\,a<x<b\}$.

(2) Closed interval : Let a and b be two real numbers such that $a<b,$ then the set of all real numbers lying between $a$ and $b$ including $a$ and $b$ is called a closed interval and is denoted by $[a,\,\,b]$. Thus, $[a,\,\,b]=\{x\in R\,:\,a\le x\le b\}$

(3) Open-Closed interval : It is denoted by $[a,\,\,b]$ or $(a,\,\,b]$ and $[a,\,\,b]$ or $(a,\,\,b]=\{x\in R\,:\,\,a<x\le b\}$.

(4) Closed-Open interval : It is denoted by $[a,\,\,b]$ or $[a,\,\,b)$ and  $[a,\,\,b]$ or $[a,\,\,b)=\{x\in R\,:\,\,a\le x<b\}$

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