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In mathematics, a family, or indexed family, is informally a collection of objects, each associated with an index from some index set.For example, a family of real numbers, indexed by the set of integers, is a collection of real numbers, where a given function selects one real number for each integer (possibly the same) as indexing.
In combinatorics, a Helly family of order k is a family of sets in which every minimal subfamily with an empty intersection has k or fewer sets in it. Equivalently, every finite subfamily such that every k-fold intersection is non-empty has non-empty total intersection. [1] The k-Helly property is the property of being a Helly family of order k ...
Additionally, a family of sets may be defined as a function from a set , known as the index set, to , in which case the sets of the family are indexed by members of . [1] In some contexts, a family of sets may be allowed to contain repeated copies of any given member, [ 2 ] [ 3 ] [ 4 ] and in other contexts it may form a proper class .
A nested set collection or nested set family is a collection of sets that consists of chains of subsets forming a hierarchical structure, like Russian dolls. It is used as reference concept in scientific hierarchy definitions, and many technical approaches, like the tree in computational data structures or nested set model of relational databases .
The mathematical models used to describe the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish each spring in a lake are examples of dynamical systems. List of dynamical systems and differential equations topics; List of nonlinear partial differential equations; List of partial differential equation topics
Americans said they are the most grateful for family and friends, 79 percent. Seventy-one percent said they were most grateful for health while freedom ranked third at 58 percent, according to the ...
Algebraic functions are functions that can be expressed as the solution of a polynomial equation with integer coefficients.. Polynomials: Can be generated solely by addition, multiplication, and raising to the power of a positive integer.
The choice affects your entire family, including your children's chance to make memories with their extended family and your wife's ability to enjoy time with the people she loves.
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