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Mediant (mathematics)

In mathematics, the mediant of two fractions, generally made up of four positive integers and is defined as That is to say, the numerator and denominator of the mediant are the sums of the numerators

Falling and rising factorials

In mathematics, the falling factorial (sometimes called the descending factorial, falling sequential product, or lower factorial) is defined as the polynomial The rising factorial (sometimes called th

Least common multiple

In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer

Shifting nth root algorithm

The shifting nth root algorithm is an algorithm for extracting the nth root of a positive real number which proceeds iteratively by shifting in n digits of the radicand, starting with the most signifi

Empty sum

In mathematics, an empty sum, or nullary sum, is a summation where the number of terms is zero. The natural way to extend non-empty sums is to let the empty sum be the additive identity. Let , , , ...

Proofs involving the addition of natural numbers

This article contains mathematical proofs for some properties of addition of the natural numbers: the additive identity, commutativity, and associativity. These proofs are used in the article Addition

Stirling numbers of the second kind

In mathematics, particularly in combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of n objects into k non-empty subsets and is

Binomial coefficient

In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers n ≥ k ≥ 0 and

Operation (mathematics)

In mathematics, an operation is a function which takes zero or more input values (also called "operands" or "arguments") to a well-defined output value. The number of operands is the arity of the oper

Pythagorean addition

In mathematics, Pythagorean addition is a binary operation on the real numbers that computes the length of the hypotenuse of a right triangle, given its two sides. According to the Pythagorean theorem

Quotition and partition

In arithmetic, quotition and partition are two ways of viewing fractions and division. In quotition division one asks, "how many parts are there?"; While in partition division one asks, "what is the s

Hyperoperation

In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations in this context) that starts with a unary operation (the successor function with n

Modulo operation

In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another (called the modulus of the operation). Given two positive numbers a a

Running total

A running total is the summation of a sequence of numbers which is updated each time a new number is added to the sequence, by adding the value of the new number to the previous running total. Another

Pentation

In mathematics, pentation (or hyper-5) is the next hyperoperation after tetration and before hexation. It is defined as iterated (repeated) tetration, just as tetration is iterated exponentiation. It

Tetration

In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no standard notation for tetration, though and the left-exponent xb are common. Under th

Stirling numbers of the first kind

In mathematics, especially in combinatorics, Stirling numbers of the first kind arise in the study of permutations. In particular, the Stirling numbers of the first kind count permutations according t

Nth root

In mathematics, an nth root of a number x is a number r which, when raised to the power n, yields x: where n is a positive integer, sometimes called the degree of the root. A root of degree 2 is calle

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