Real numbers are numbers that can be expressed as decimals, such as
A real number can be represented geometrically as a point on number line called real line.
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Set of real numbers consists of all rational and all irrational numbers.
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].
