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Any two objects have a pair. The set {A,A} is abbreviated {A}, called the singleton containing A. Note that a singleton is a special case of a pair. Being able to construct a singleton is necessary, for example, to show the non-existence of the infinitely descending chains = {} from the Axiom of regularity.
The syntax of JavaScript is the set of rules that define a correctly structured JavaScript program. The examples below make use of the log function of the console object present in most browsers for standard text output. The JavaScript standard library lacks an official standard text output function (with the exception of document.write).
A matching is a bijection from the elements of one set to the elements of the other set. A matching is not stable if: There is an element A of the first matched set which prefers some given element B of the second matched set over the element to which A is already matched, and
Suppose that one wants to define what it means for two sets to "have the same number of elements". One way to do this is to say that two sets "have the same number of elements", if and only if all the elements of one set can be paired with the elements of the other, in such a way that each element is paired with exactly one element.
More generally, a pairing function on a set is a function that maps each pair of elements from into an element of , such that any two pairs of elements of are associated with different elements of , [5] [a] or a bijection from to .
A property, in some object-oriented programming languages, is a special sort of class member, intermediate in functionality between a field (or data member) and a method.The syntax for reading and writing of properties is like for fields, but property reads and writes are (usually) translated to 'getter' and 'setter' method calls.
A set with precisely two elements is also called a 2-set or (rarely) a binary set. An unordered pair is a finite set; its cardinality (number of elements) is 2 or (if the two elements are not distinct) 1. In axiomatic set theory, the existence of unordered pairs is required by an axiom, the axiom of pairing.
In set theory in mathematics and formal logic, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets are sets whose intersection is the empty set. [1] For example, {1, 2, 3} and {4, 5, 6} are disjoint sets, while {1, 2, 3} and {3, 4, 5} are not disjoint. A collection of two or more sets is ...