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# INTERVALS

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(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 $$\left( a,\,\,b \right)=\left\{ x:x\in \text{R},a<x<b \right\}$$

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

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

•  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:

$$\displaystyle \left\{ x:x\in \text{R},-2<x\le 3 \right\}=\left( -2,3 \right]$$

$$\begin{array}{l}\left\{ x:x\in \text{R},-2\le x\le 1\, \right\}=\left[ -2,1 \right]\\\left\{ x:x\in R,-1<x<1 \right\}\,\,\,=\left( -1,\,\,1 \right)\\\left\{ x:x\in \text{R,}\,\text{0}\,\le \,x<5 \right\}\,\,\,\,\,\,=\left[ 0,5 \right)\end{array}$$

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