## INTERVALS

(1) Closed Interval: Let a and b are two given real numbers such that $\text{a}\,\text{}\,\text{b}$ , then $\left[ \text{a,}\,\text{b} \right]=\left\{ x:x\in \text{R},\,a\le x\le b \right\}$

(2) Open Interval: Let a and b are two given real numbers such that $\text{a}\,\text{}\,\text{b,}$ then $\left] a,b \right[$ or $\left( a,\,\,b \right)=\left\{ x:x\in \text{R},a

(3) Closed-open Interval: Let a and b are two given real numbers such that $a, then $\displaystyle \left[ a,b \right[\,\,\text{or}\,\,\left[ a,\,\,b \right)=\{x:x\in \text{R},a\le x

(4) Open-closed Interval: Let a and b are two given real numbers such that $a then $\left] a,b \right]\,\,\,or\,\,\left( a,\,b \right]\,\,=\,\left\{ x:\,x\in \,\text{R,}\,a

•  Real number, R represented as $\left( -\infty ,\,\infty \right)$
• ${{\text{R}}^{\text{+}}}$ can be represented as $[0,\,\,\infty )$
• ${{\text{R}}^{-}}$can be represented as $[-\infty ,\,0)$
• We can’t represent Natural numbers, Integers, whole numbers in intervals.

Examples:

$\displaystyle \left\{ x:x\in \text{R},-2

$\begin{array}{l}\left\{ x:x\in \text{R},-2\le x\le 1\, \right\}=\left[ -2,1 \right]\\\left\{ x:x\in R,-1