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A Venn diagram, also called a set diagram or logic diagram, shows all possible logical relations between a finite collection of different sets. These diagrams depict elements as points in the plane, and sets as regions inside closed curves. A Venn diagram consists of multiple overlapping closed curves, usually circles, each representing a set.
In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. [5] A set may have a finite number of elements or be an infinite set.
Set theory begins with a fundamental binary relation between an object o and a set A. If o is a member (or element) of A, the notation o ∈ A is used. A set is described by listing elements separated by commas, or by a characterizing property of its elements, within braces { }. Since sets are objects, the membership relation can relate sets as ...
Inclusion–exclusion principle. In combinatorics, a branch of mathematics, the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as. where A and B are two finite sets and | S | indicates the cardinality of a ...
Given p ∈ P, the set {x : p ≤ x} is the smallest filter containing p, and sometimes written ↑ p. Such a filter is called a principal filter; p is said to be the principal element of F, or generate F. Refinement. Suppose B and C are two prefilters on P, and, for each c ∈ C, there is a b ∈ B, such that b ≤ c.
Ideal (order theory) In mathematical order theory, an ideal is a special subset of a partially ordered set (poset). Although this term historically was derived from the notion of a ring ideal of abstract algebra, it has subsequently been generalized to a different notion. Ideals are of great importance for many constructions in order and ...
The Pareto principle may apply to fundraising, i.e. 20% of the donors contributing towards 80% of the total. The Pareto principle (also known as the 80/20 rule, the law of the vital few and the principle of factor sparsity [1] [2]) states that for many outcomes, roughly 80% of consequences come from 20% of causes (the "vital few"). [1]
Since (fg) = (f) + (g), the set of principal divisors is a subgroup of the group of divisors. Two divisors that differ by a principal divisor are called linearly equivalent . On a compact Riemann surface, the degree of a principal divisor is zero; that is, the number of zeros of a meromorphic function is equal to the number of poles, counted ...