indexed family वाक्य
उदाहरण वाक्य
मोबाइल
- Formally, an indexed family is the same thing as a image of the family's underlying function is an element of the family.
- Sometimes it is useful to consider all functions with certain parameters as " parametric family ", i . e . as an indexed family of functions.
- For many purposes, the particular choice of auxiliary index is unimportant, and in a simplifying abuse of notation, the indexed family can be treated simply as a collection of sets.
- Given an indexed family of objects A _ i, indexed with i \ in I, the direct sum may be written \ textstyle A = \ bigoplus _ { i \ in I } A _ i.
- An object is the product of a family of objects iff there exist morphisms, such that for every object and a-indexed family of morphisms there exists a unique morphism such that the following diagrams commute for all:
- An indexed family,, where is in some index-set, may define a multiset, sometimes written } }, in which the multiplicity of any element is the number of indices such that a _ i = x.
- Hence, an indexed family of sets is conceptually different from a family of sets ( which is just a synonym for " set of sets " ), but in practice the distinction is sometimes fuzzy and the indexed family is identified with its range and treated like an ordinary family.
- Hence, an indexed family of sets is conceptually different from a family of sets ( which is just a synonym for " set of sets " ), but in practice the distinction is sometimes fuzzy and the indexed family is identified with its range and treated like an ordinary family.
- It states that for every indexed family ( S _ i ) _ { i \ in I } of nonempty sets there exists an indexed family ( x _ i ) _ { i \ in I } of elements such that x _ i \ in S _ i for every i \ in I.
- It states that for every indexed family ( S _ i ) _ { i \ in I } of nonempty sets there exists an indexed family ( x _ i ) _ { i \ in I } of elements such that x _ i \ in S _ i for every i \ in I.
- The support for derived instances of Eq and Show makes their methods = = and show generic in a qualitatively different way from parametrically polymorphic functions : these " functions " ( more accurately, type-indexed families of functions ) can be applied to values of various types, and although they behave differently for every argument type, little work is needed to add support for a new type.
- For this we consider structures \ langle X, ( R _ i ) _ I, \ mathcal { F } \ rangle where \ langle X, ( R _ i ) _ I \ rangle is a relational structure i . e . a set with an indexed family of relations defined on it, and \ langle X, \ mathcal { F } \ rangle is a field of sets.
- The supremum of a " directed family of simple valuations " ( i . e . an indexed family of simple valuations which is also directed in the sense that for each pair of indexes i and j belonging to the index set I, there exists an index k such that \ scriptstyle v _ i ( U ) \ leq v _ k ( U ) \ ! and \ scriptstyle v _ j ( U ) \ subseteq v _ k ( U ) \ ! ) is called "'quasi-simple valuation "'
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