Real Numbers

Real Numbers

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

4/5 = 0.8000...

1/3 = 0.3333...

√2 = 1.4142...

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

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

1. {x : x ∈ R, a ≤ x ≤ b} is called a closed interval and is denoted by [a, b].
2. {x : x ∈ R, a < x < b} is called an open interval and is denoted by (a, b).
3. {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.
4. {x : x ∈ R, a < x ≤ b} is called left open and right closed interval and is denoted by (a, b].