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Function (mathematics) and Von Neumann–Bernays–Gödel set theory

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Function (mathematics) and Von Neumann–Bernays–Gödel set theory

Function (mathematics) vs. Von Neumann–Bernays–Gödel set theory

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity. In the foundations of mathematics, von Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel set theory (ZFC).

Similarities between Function (mathematics) and Von Neumann–Bernays–Gödel set theory

Function (mathematics) and Von Neumann–Bernays–Gödel set theory have 22 things in common (in Unionpedia): Axiom of choice, Binary relation, Class (set theory), Empty set, Foundations of mathematics, Identity function, Intersection (set theory), Mathematical analysis, Mathematical induction, Morphism, Natural number, Nicolas Bourbaki, Operation (mathematics), Ordered pair, Power set, Recursion, Set (mathematics), Set theory, Surjective function, Tuple, Union (set theory), Well-order.

Axiom of choice

In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty.

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Binary relation

In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.

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Class (set theory)

In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share.

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Empty set

In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.

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Foundations of mathematics

Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics.

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Identity function

Graph of the identity function on the real numbers In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument.

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Intersection (set theory)

In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.

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Mathematical analysis

Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

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Mathematical induction

Mathematical induction is a mathematical proof technique.

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Morphism

In mathematics, a morphism is a structure-preserving map from one mathematical structure to another one of the same type.

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Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

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Nicolas Bourbaki

Nicolas Bourbaki is the collective pseudonym under which a group of (mainly French) 20th-century mathematicians, with the aim of reformulating mathematics on an extremely abstract and formal but self-contained basis, wrote a series of books beginning in 1935.

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Operation (mathematics)

In mathematics, an operation is a calculation from zero or more input values (called operands) to an output value.

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Ordered pair

In mathematics, an ordered pair (a, b) is a pair of objects.

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Power set

In mathematics, the power set (or powerset) of any set is the set of all subsets of, including the empty set and itself, variously denoted as, 𝒫(), ℘() (using the "Weierstrass p"),,, or, identifying the powerset of with the set of all functions from to a given set of two elements,.

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Recursion

Recursion occurs when a thing is defined in terms of itself or of its type.

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Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

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Set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

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Surjective function

In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x).

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Tuple

In mathematics, a tuple is a finite ordered list (sequence) of elements.

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Union (set theory)

In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.

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Well-order

In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering.

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The list above answers the following questions

Function (mathematics) and Von Neumann–Bernays–Gödel set theory Comparison

Function (mathematics) has 160 relations, while Von Neumann–Bernays–Gödel set theory has 146. As they have in common 22, the Jaccard index is 7.19% = 22 / (160 + 146).

References

This article shows the relationship between Function (mathematics) and Von Neumann–Bernays–Gödel set theory. To access each article from which the information was extracted, please visit:

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