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40 relations: Axiom schema of specification, Cartesian product, Colon (punctuation), Computer science, Element (mathematics), Ellipsis, Empty set, Existential quantification, Filter (higher-order function), Function (mathematics), Generator (computer programming), Glossary of set theory, Haskell (programming language), Integer, Intension, List (abstract data type), List comprehension, Logic, Logical conjunction, Map (higher-order function), Mathematical notation, Mathematics, Monad (functional programming), Natural number, Parity (mathematics), Predicate (mathematical logic), Programming language, Python (programming language), Rational number, Real number, Russell's paradox, Scala (programming language), Set (mathematics), Set notation, Set theory, Sign (mathematics), Vertical bar, Z notation, Zermelo–Fraenkel set theory, Zero element.
Axiom schema of specification
In many popular versions of axiomatic set theory the axiom schema of specification, also known as the axiom schema of separation, subset axiom scheme or axiom schema of restricted comprehension is an axiom schema.
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Cartesian product
In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.
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Colon (punctuation)
The colon is a punctuation mark consisting of two equally sized dots centered on the same vertical line.
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Computer science
Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.
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Element (mathematics)
In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.
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Ellipsis
An ellipsis (plural ellipses; from the ἔλλειψις, élleipsis, 'omission' or 'falling short') is a series of dots (typically three, such as "…") that usually indicates an intentional omission of a word, sentence, or whole section from a text without altering its original meaning.
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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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Existential quantification
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some".
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Filter (higher-order function)
In functional programming, filter is a higher-order function that processes a data structure (usually a list) in some order to produce a new data structure containing exactly those elements of the original data structure for which a given predicate returns the boolean value true.
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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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Generator (computer programming)
In computer science, a generator is a special routine that can be used to control the iteration behaviour of a loop.
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Glossary of set theory
This is a glossary of set theory.
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Haskell (programming language)
Haskell is a standardized, general-purpose compiled purely functional programming language, with non-strict semantics and strong static typing.
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Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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Intension
In linguistics, logic, philosophy, and other fields, an intension is any property or quality connoted by a word, phrase, or another symbol.
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List (abstract data type)
In computer science, a list or sequence is an abstract data type that represents a countable number of ordered values, where the same value may occur more than once.
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List comprehension
A list comprehension is a syntactic construct available in some programming languages for creating a list based on existing lists.
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Logic
Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.
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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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Map (higher-order function)
In many programming languages, map is the name of a higher-order function that applies a given function to each element of a list, returning a list of results in the same order.
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Mathematical notation
Mathematical notation is a system of symbolic representations of mathematical objects and ideas.
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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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Monad (functional programming)
In functional programming, a monad is a design pattern that defines how functions, actions, inputs, and outputs can be used together to build generic types, with the following organization.
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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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Parity (mathematics)
In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd.
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Predicate (mathematical logic)
In mathematical logic, a predicate is commonly understood to be a Boolean-valued function P: X→, called the predicate on X. However, predicates have many different uses and interpretations in mathematics and logic, and their precise definition, meaning and use will vary from theory to theory.
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Programming language
A programming language is a formal language that specifies a set of instructions that can be used to produce various kinds of output.
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Python (programming language)
Python is an interpreted high-level programming language for general-purpose programming.
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Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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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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Scala (programming language)
Scala is a general-purpose programming language providing support for functional programming and a strong static type system.
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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 notation
Sets are fundamental objects in mathematics.
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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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Sign (mathematics)
In mathematics, the concept of sign originates from the property of every non-zero real number of being positive or negative.
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Vertical bar
The vertical bar (|) is a computer character and glyph with various uses in mathematics, computing, and typography.
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Z notation
The Z notation is a formal specification language used for describing and modelling computing systems.
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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.
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Zero element
In mathematics, a zero element is one of several generalizations of the number zero to other algebraic structures.
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Set abstraction, Set builder, Set builder notation, Set comprehension, Set-builder.
References
[1] https://en.wikipedia.org/wiki/Set-builder_notation
