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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]
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.
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.
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
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var x1 = 0; // A global variable, because it is not in any function let x2 = 0; // Also global, this time because it is not in any block function f {var z = 'foxes', r = 'birds'; // 2 local variables m = 'fish'; // global, because it wasn't declared anywhere before function child {var r = 'monkeys'; // This variable is local and does not affect the "birds" r of the parent function. z ...