NumbersWiki:About

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This page is about real and imaginary numbers 

In mathematics, a real number is a value of a continuing quantity that can represent a distance along a line (or alternatively, a quantity that can be represented as an infinite decimal expansion). 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 and the fraction 4/3, and all irrational numbers, such as  (1.414213..., the square root of 2, an irrational algebraic number).

Included within the irrationals are the real transcendental numbers, such as π (3.141592...). Distance is measured, real numbers can be used to measure quantities such as time, mass, energy, velocity, and beyond. A set of real numbers is denoted using the symbol R or  and is often called "the reals".

Real numbers are 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 7.6321234, where each sequence digit is measured in units one-tenth the size of the previous one. The real line may be thought of as a part of the complex plane, and the real numbers can be thought of as a part of the complex numbers.''

Citation MIT Lecture 21 Educational Math Lecture

Set of Real Numbers
This is a table of Categories, definitions, and examples of Real numbers. Real numbers include both rational an irrational number.

If we toss three coins. We can let R equals the number of heads among the three coins. This would use rational numbers.

The opposite of a Real number is an imaginary number. Rene Descartes coined this term.

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i2 = −1. The square of an imaginary number bi is −b2. For example, 5i is an imaginary number, and its square is −25. By definition, zero is considered to be both real and imaginary.

Originally coined in the 17th century by René Descartes[4] as a derogatory term and regarded as fictitious or useless, the concept gained wide acceptance following the work of Leonhard Euler (in the 18th century) and Augustin-Louis Cauchy and Carl Friedrich Gauss (in the early 19th century).

An imaginary number bi can be added to a real number a to form a complex number of the form a + bi, where the real numbers a and b are called, respectively, the real part and the imaginary part of the complex number. Citation wikipedia