# Number System - Real Number (Scalar) - $\mathbb{R}$

A real number $\mathbb{R}$ is a value that represents a quantity along a line.

They have been called real to distinguish them from imaginary number.

The adjective real in this context was introduced in the 17th century by René Descartes, who distinguished between real and imaginary roots of polynomials.

The real numbers include all the rational numbers, such as:

• the integer −5
• the fraction 4/3,
• the irrational numbers, such as √2 (1.41421356…)

Real numbers can be thought of as points on an infinitely long line called the number line or real line, where the points corresponding to integers are equally spaced.

Any real number can be determined by a possibly infinite decimal representation, such as that of 8.632.

Since the set of rational numbers is countable, and the set of real numbers is uncountable, almost all real numbers are irrational

## 3 - Character

• 211D - $\mathbb{R}$

## 4 - Scalar

In linear algebra, real numbers are called scalars and relate to vectors in a vector space through the operation of scalar multiplication.

Greek letters ($\alpha, \beta, \gamma$) denote scalars.

## 5 - Associativity

real numbers are associative, meaning that for any real numbers x, y, and z, it’s always the case that (x + y) + z = x + (y + z).