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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. More generally, an unordered n-tuple is a set of the form {a 1, a 2,... a n}. [5] [6] [7]
Example of a web form with name-value pairs. A name–value pair, also called an attribute–value pair, key–value pair, or field–value pair, is a fundamental data representation in computing systems and applications. Designers often desire an open-ended data structure that allows for future extension without modifying existing code or data.
The concept of "unobtrusiveness" in relation to client-side JavaScript was coined in 2002 by Stuart Langridge [7] in the article "Unobtrusive DHTML, and the power of unordered lists". [8] In the article Langridge argued for a way to keep all JavaScript code, including event handlers, outside of the HTML when using dynamic HTML (DHTML). [7]
HTML tags most commonly come in pairs like < h1 > and </ h1 >, although some represent empty elements and so are unpaired, for example < img >. The first tag in such a pair is the start tag , and the second is the end tag (they are also called opening tags and closing tags ).
In the second example above, the numbering resets after the blank line. This problem is less noticeable with other list types, but it still affects the underlying HTML code and may have disruptive effects for some readers; see WP:LISTGAP for details. In order to be a list, each line must begin the same way. This holds true for mixed lists.
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
The axiom of pairing is generally considered uncontroversial, and it or an equivalent appears in just about any axiomatization of set theory. Nevertheless, in the standard formulation of the Zermelo–Fraenkel set theory, the axiom of pairing follows from the axiom schema of replacement applied to any given set with two or more elements, and thus it is sometimes omitted.
Theorem: If A and B are sets, then there is a set A×B which consists of all ordered pairs (a, b) of elements a of A and b of B. Proof: The singleton set with member a, written {a}, is the same as the unordered pair {a, a}, by the axiom of extensionality. The singleton, the set {a, b}, and then also the ordered pair