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\}

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(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\}

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(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\}

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(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\}

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  •  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}

Post Author: E-Maths