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Information about Index Set

In mathematics, the elements of a set A may be indexed or labeled by means of a set J that is on that account called an index set. The indexing consists of a surjective function from J onto A and the indexed collection is typically called an (indexed) family, often written as (Aj)j∈J.

Examples



The set of all the functions is an uncountable set indexed by .

See also

Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions".
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SET may stand for:
  • Sanlih Entertainment Television, a television channel in Taiwan
  • Secure electronic transaction, a protocol used for credit card processing,

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non-surjective function.]] In mathematics, a function f is said to be surjective if its values span its whole codomain; that is, for every y in the codomain, there is at least one x in the domain such that f(x) = y .
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Family in mathematics may have one of the following meanings
  • Set (mathematics)
  • multiset (collection)
  • Indexed family
  • Family of sets

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enumeration of a set is either a procedure for listing all members of the set in some definite sequence, or a count of objects of a specified kind. The two kinds of enumeration often, but not always, overlap.
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countable set is a set with the same cardinality (i.e., number of elements) as some subset of the set of natural numbers. The term was originated by Georg Cantor; it stems from the fact that the natural numbers are often called counting numbers.
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indicator function or a characteristic function is a function defined on a set that indicates membership of an element in a subset of .

The indicator function of a subset of a set is a function



defined as


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uncountable set is an infinite set which is too big to be countable. The uncountability of a set is closely related to its cardinal number; a set is uncountable if its cardinal number is larger than that of the natural numbers.
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For other uses of "Index", see Index.


The word index is used in variety of senses in mathematics.
  • In perhaps the most frequent sense, an index is a superscript or subscript to a symbol.

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In mathematics, an indexed family of sets is defined in stages, beginning with the more general concept of an indexed family of elements, which is really just an alternative way of conceptualizing a function or a mapping.
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