**Real Number Set Diagram**: this diagram is one of our most searched charts and infographics by people seeking to learn about new things and improve their general knowledge of how the world works.

The Real Number Set is a fundamental concept in mathematics that is used to represent all possible values of a continuous one-dimensional quantity such as distance, duration, or temperature . It is denoted by the symbol R and is defined as the set of all rational and irrational numbers .

A real number can be almost uniquely represented by an infinite decimal expansion . 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 . The set of real numbers is sometimes called “the reals” .

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 of 2 = 1.414…; these are called algebraic numbers. There are also real numbers which are not, such as ? = 3.1415…; these are called transcendental numbers .

Real numbers can be thought of as all points on a line called the number line or real line, where the points corresponding to integers (…, -2, -1, 0, 1, 2, …) are equally spaced. Conversely, analytic geometry is the association of points on lines (especially axis lines) to real numbers such that geometric displacements are proportional to differences between corresponding numbers .

Real numbers are completely characterized by their fundamental properties that can be summarized by saying that they form an ordered field that is Dedekind complete . This implies that one can manipulate real numbers and compute with them, without knowing how they can be defined . Real numbers are used in many areas of mathematics, including algebra, geometry, calculus, and analysis .

In summary, the Real Number Set is a set of all possible values of a continuous one-dimensional quantity. It includes