Real Numbers Class 10 - Free Master Class

We will study the basics of real numbers today.

In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature. Here, continuous means that pairs of values can have arbitrarily small differences.[a] Every real number can be almost uniquely represented by an infinite decimal expansion.[b][1]

The real numbers are fundamental in calculus (and more generally in all mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives.[c]

The set of real numbers, sometimes called "the reals", is traditionally denoted by a bold R, often using blackboard bold, {\displaystyle \mathbb {R} }{\displaystyle \mathbb {R} }.[2][3] The adjective real, used in the 17th century by René Descartes, distinguishes real numbers from imaginary numbers such as the square roots of −1.[4]

The real numbers include the rational numbers, such as the integer −5 and the fraction 4 / 3. The rest of the real numbers are called irrational numbers. Some irrational numbers (as well as all the rationals) are the root of a polynomial with integer coefficients, such as the square root √2 = 1.414...; these are called algebraic numbers. There are also real numbers which are not, such as π = 3.1415...; these are called transcendental numbers.[4]