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...

Informally, a definable real number is a real number that can be uniquely specified by its description. The description may be expressed as a construction...

In mathematics, the extended real number system is obtained from the real number system R {\displaystyle \mathbb {R} } by adding two elements denoted...

In number theory, a number field F is called totally real if for each embedding of F into the complex numbers the image lies inside the real numbers....

π: Every point of the number line corresponds to a unique real number, and every real number to a unique point. Using a number line, numerical concepts...

numbers are an extension of the real numbers to include certain classes of infinite and infinitesimal numbers. A hyperreal number x {\displaystyle x} is said...

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary...

recursive numbers, effective numbers, computable reals, or recursive reals. The concept of a computable real number was introduced by Émile Borel in 1912, using...

bi, the real number a is called the real part and b is called the imaginary part. If the real part of a complex number is 0, then the number is called...

rational number is a real number. The real numbers that are rational are those whose decimal expansion either terminates after a finite number of digits...

In mathematics, a transcendental number is a real or complex number that is not algebraic: that is, not the root of a non-zero polynomial with integer...

imaginary number is the product of a real number and the imaginary unit i, which is defined by its property i2 = −1. The square of an imaginary number bi is...

In mathematics, there are several equivalent ways of defining the real numbers. One of them is that they form a complete ordered field that does not contain...

property of the real numbers that, intuitively, implies that there are no "gaps" (in Dedekind's terminology) or "missing points" in the real number line. This...

number (i) is a solution to the quadratic equation x2 + 1 = 0. Although there is no real number with this property, i can be used to extend the real numbers...

values 0, 1 and ∞. The projectively extended real number line is distinct from the affinely extended real number line, in which +∞ and −∞ are distinct. Unlike...

sometimes is called a fractional number. Decimals are commonly used to approximate real numbers. By increasing the number of digits after the decimal separator...

In mathematics, the sign of a real number is its property of being either positive, negative, or 0. Depending on local conventions, zero may be considered...

In mathematics, the absolute value or modulus of a real number x {\displaystyle x} , denoted | x | {\displaystyle |x|} , is the non-negative value of...

are irrational. Like all real numbers, irrational numbers can be expressed in positional notation, notably as a decimal number. In the case of irrational...

while infinity is commonly defined either as an extreme limit of the real number line (applied to a function or sequence that "diverges to infinity" or...

In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus...

mathematics, hypercomplex number is a traditional term for an element of a finite-dimensional unital algebra over the field of real numbers. The study of...

A real data type is a data type used in a computer program to represent an approximation of a real number. Because the real numbers are not countable...

In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word infinitesimal comes from...

positive real axis, and is usually drawn as a horizontal ray. This ray is used as reference in the polar form of a complex number. The real positive axis...

mathematics, a real interval is the set of all real numbers lying between two fixed endpoints with no "gaps". Each endpoint is either a real number or positive...

integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 has the result 0, and...

mathematics, a negative number is the opposite (mathematics) of a positive real number. Equivalently, a negative number is a real number that is less than zero...

functions. The theorems of real analysis rely on the properties of the real number system, which must be established. The real number system consists of an...