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In prime factorization, the multiplicity of a prime factor is its -adic valuation.For example, the prime factorization of the integer 60 is . 60 = 2 × 2 × 3 × 5, the multiplicity of the prime factor 2 is 2, while the multiplicity of each of the prime factors 3 and 5 is 1.
The real numbers (extended by +∞) with the operations of minimum and addition form a semiring, called the min tropical semiring, [e] and a valuation v is almost a semiring homomorphism from K to the tropical semiring, except that the homomorphism property can fail when two elements with the same valuation are added together.
The multiplicity of a prime factor p in n, that is the largest exponent m for which p m divides n. a 0 (n) – the sum of primes dividing n counting multiplicity, sometimes called sopfr(n), the potency of n or the integer logarithm of n (sequence A001414 in the OEIS). For example: a 0 (4) = 2 + 2 = 4 a 0 (20) = a 0 (2 2 · 5) = 2 + 2 + 5 = 9 a ...
For example, a polynomial of degree n has a pole of degree n at infinity. The complex plane extended by a point at infinity is called the Riemann sphere. If f is a function that is meromorphic on the whole Riemann sphere, then it has a finite number of zeros and poles, and the sum of the orders of its poles equals the sum of the orders of its ...
Multiplicity (informatics), a type of relationship in class diagrams for Unified Modeling Language used in software engineering; Multiplicity (mathematics), the number of times an element is repeated in a multiset; Multiplicity (software), a software application which allows a user to control two or more computers from one mouse and keyboard
In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, [1] allows for multiple instances for each of its elements.The number of instances given for each element is called the multiplicity of that element in the multiset.
This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of an isolated but particularly striking fact, as opposed to a proof of a ...
Multiplicity (French: multiplicité) is a philosophical concept developed by Edmund Husserl and Henri Bergson from Riemann's description of the mathematical concept. [1] In his essay The Idea of Duration, Bergson discusses multiplicity in light of the notion of unity. Whereas a unity refers to a given thing in as far as it is a whole ...