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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 bag-of-words model (BoW) is a model of text which uses an unordered collection (a "bag") of words. It is used in natural language processing and information retrieval (IR). It disregards word order (and thus most of syntax or grammar) but captures multiplicity .
A Base64-encoded binary MD5 sum of the content of the response: Content-MD5: Q2hlY2sgSW50ZWdyaXR5IQ== Obsolete [15] RFC 1544, 1864, 4021: Content-Range: Where in a full body message this partial message belongs: Content-Range: bytes 21010-47021/47022: Permanent RFC 9110: Content-Type: The MIME type of this content: Content-Type: text/html ...
For example, to prove the case n = 3, use the axiom of pairing three times, to produce the pair {A 1,A 2}, the singleton {A 3}, and then the pair {{A 1,A 2},{A 3}}. The axiom of union then produces the desired result, {A 1,A 2,A 3}. We can extend this schema to include n=0 if we interpret that case as the axiom of empty set.
HTML element content categories. HTML documents imply a structure of nested HTML elements. These are indicated in the document by HTML tags, enclosed in angle brackets. [73] [better source needed] In the simple, general case, the extent of an element is indicated by a pair of tags: a "start tag" < p > and "end tag" </ p >. The text content of ...
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
There are three types of lists: unordered lists, ordered lists, and description lists (a.k.a. definition lists or association lists). In the following sections, various list types are used for different examples, but other list types will generally give corresponding results.