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The carrier (underlying set) associated with a unit type can be any singleton set. There is an isomorphism between any two such sets, so it is customary to talk about the unit type and ignore the details of its value. One may also regard the unit type as the type of 0-tuples, i.e. the product of no types.
A set such as {{,,}} is a singleton as it contains a single element (which itself is a set, but not a singleton). A set is a singleton if and only if its cardinality is 1. In von Neumann's set-theoretic construction of the natural numbers, the number 1 is defined as the singleton {}.
A class diagram exemplifying the singleton pattern.. In object-oriented programming, the singleton pattern is a software design pattern that restricts the instantiation of a class to a singular instance.
The J programming language is a descendant of APL but uses the ASCII character set rather than APL symbols. Because the printable range of ASCII is smaller than APL's specialized set of symbols, . (dot) and : (colon) characters are used to inflect ASCII symbols, effectively interpreting unigraphs, digraphs or rarely trigraphs as standalone ...
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
Example of Kleene star applied to the empty set: ∅ * = {ε}. Example of Kleene plus applied to the empty set: ∅ + = ∅ ∅ * = { } = ∅, where concatenation is an associative and noncommutative product. Example of Kleene plus and Kleene star applied to the singleton set containing the empty string:
The empty set is the unique initial object in Set, the category of sets. Every one-element set ( singleton ) is a terminal object in this category; there are no zero objects. Similarly, the empty space is the unique initial object in Top , the category of topological spaces and every one-point space is a terminal object in this category.
[2] [3] [4] Functionally, the mutator pop can be interpreted as the pair of selectors (pick, rest), where rest returns the set consisting of all elements except for the arbitrary element. [5] Can be interpreted in terms of iterate. [a] map(F,S): returns the set of distinct values resulting from applying function F to each element of S.