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Real Numbers

Relation and function of Class 12

Real numbers are numbers that can be expressed as decimals, such as

Real Numbers = 0.8000………..

Real Numbers = 0.3333………..

Real Numbers = 1.4142………..

A real number can be represented geometrically as a point on number line called real line.

Real Numbers

Set of real numbers consists of all rational and all irrational numbers.

Intervals

A subset of real line is called an interval if it contains all the real numbers lying between every pair of its elements.

Let a, b ∈ R. Then the set

(i) {x : x ∈ R, a ≤ x ≤ b} is called a closed interval and is denoted by [a, b].

(ii) {x : x ∈ R, a < x < b} is called an open interval and is denoted by (a, b).

(iii) {x : x ∈ R, a ≤ x < b} is called semi-closed or semi-open interval and is denoted by
[a, b). It is also called left closed and right open interval.

(iv) {x : x ∈ R, a < x ≤ b} is called left open and right closed interval and is denoted by (a, b].

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