Axiom of extensionality and Constructible universe

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

Difference between Axiom of extensionality and Constructible universe

Axiom of extensionality vs. Constructible universe

In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of extensionality, or axiom of extension, is one of the axioms of Zermelo–Fraenkel set theory. In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted L, is a particular class of sets that can be described entirely in terms of simpler sets.

Similarities between Axiom of extensionality and Constructible universe

Axiom of extensionality and Constructible universe have 7 things in common (in Unionpedia): Axiom, Axiom of regularity, Formal language, Mathematics, Set (mathematics), Set theory, Zermelo–Fraenkel set theory.

Axiom

An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.

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Axiom of regularity

In mathematics, the axiom of regularity (also known as the axiom of foundation) is an axiom of Zermelo–Fraenkel set theory that states that every non-empty set A contains an element that is disjoint from A. In first-order logic, the axiom reads: The axiom implies that no set is an element of itself, and that there is no infinite sequence (an) such that ai+1 is an element of ai for all i. With the axiom of dependent choice (which is a weakened form of the axiom of choice), this result can be reversed: if there are no such infinite sequences, then the axiom of regularity is true.

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Formal language

In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols together with a set of rules that are specific to it.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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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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Zermelo–Fraenkel set theory

In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.

Axiom of extensionality and Zermelo–Fraenkel set theory · Constructible universe and Zermelo–Fraenkel set theory · See more »

The list above answers the following questions

What Axiom of extensionality and Constructible universe have in common
What are the similarities between Axiom of extensionality and Constructible universe

Axiom of extensionality and Constructible universe Comparison

Axiom of extensionality has 22 relations, while Constructible universe has 66. As they have in common 7, the Jaccard index is 7.95% = 7 / (22 + 66).

References

This article shows the relationship between Axiom of extensionality and Constructible universe. To access each article from which the information was extracted, please visit:

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