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Naive set theory and Outline of logic

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

Difference between Naive set theory and Outline of logic

Naive set theory vs. Outline of logic

Naïve set theory is any of several theories of sets used in the discussion of the foundations of mathematics. Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics.

Similarities between Naive set theory and Outline of logic

Naive set theory and Outline of logic have 32 things in common (in Unionpedia): Antinomy, Begriffsschrift, Binary relation, Boolean algebra, Boolean algebra (structure), Cardinal number, Complement (set theory), Domain of discourse, Empty set, First-order logic, Function (mathematics), Gödel's incompleteness theorems, Infinite set, Intersection (set theory), Logical conjunction, Logical disjunction, Mathematics, Natural language, Negation, Ordered pair, Paradox, Partially ordered set, Power set, Russell's paradox, Set (mathematics), Set theory, Subset, Tuple, Union (set theory), Universal set, ..., Venn diagram, Zermelo–Fraenkel set theory. Expand index (2 more) »

Antinomy

Antinomy (Greek ἀντί, antí, "against, in opposition to", and νόμος, nómos, "law") refers to a real or apparent mutual incompatibility of two laws.

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Begriffsschrift

Begriffsschrift (German for, roughly, "concept-script") is a book on logic by Gottlob Frege, published in 1879, and the formal system set out in that book.

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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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Boolean algebra

In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.

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Boolean algebra (structure)

In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice.

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Cardinal number

In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets.

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Complement (set theory)

In set theory, the complement of a set refers to elements not in.

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Domain of discourse

In the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range.

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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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First-order logic

First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Gödel's incompleteness theorems

Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic.

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Infinite set

In set theory, an infinite set is a set that is not a finite set.

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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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Logical conjunction

In logic, mathematics and linguistics, And (∧) is the truth-functional operator of logical conjunction; the and of a set of operands is true if and only if all of its operands are true.

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Logical disjunction

In logic and mathematics, or is the truth-functional operator of (inclusive) disjunction, also known as alternation; the or of a set of operands is true if and only if one or more of its operands is true.

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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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Natural language

In neuropsychology, linguistics, and the philosophy of language, a natural language or ordinary language is any language that has evolved naturally in humans through use and repetition without conscious planning or premeditation.

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Negation

In logic, negation, also called the logical complement, is an operation that takes a proposition P to another proposition "not P", written \neg P (¬P), which is interpreted intuitively as being true when P is false, and false when P is true.

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Ordered pair

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

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Paradox

A paradox is a statement that, despite apparently sound reasoning from true premises, leads to an apparently self-contradictory or logically unacceptable conclusion.

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Partially ordered set

In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.

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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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Russell's paradox

In the foundations of mathematics, Russell's paradox (also known as Russell's antinomy), discovered by Bertrand Russell in 1901, showed that some attempted formalizations of the naïve set theory created by Georg Cantor led to a contradiction.

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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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Subset

In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.

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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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Universal set

In set theory, a universal set is a set which contains all objects, including itself.

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Venn diagram

A Venn diagram (also called primary diagram, set diagram or logic diagram) is a diagram that shows all possible logical relations between a finite collection of different sets.

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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.

Naive set theory and Zermelo–Fraenkel set theory · Outline of logic and Zermelo–Fraenkel set theory · See more »

The list above answers the following questions

Naive set theory and Outline of logic Comparison

Naive set theory has 97 relations, while Outline of logic has 501. As they have in common 32, the Jaccard index is 5.35% = 32 / (97 + 501).

References

This article shows the relationship between Naive set theory and Outline of logic. To access each article from which the information was extracted, please visit:

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