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An extensional definition gives meaning to a term by specifying its extension, that is, every object that falls under the definition of the term in question.. For example, an extensional definition of the term "nation of the world" might be given by listing all of the nations of the world, or by giving some other means of recognizing the members of the corresponding class.
This area also includes one of order theory's most famous open problems, the 1/3–2/3 conjecture, which states that in any finite partially ordered set that is not totally ordered there exists a pair (,) of elements of for which the linear extensions of in which < number between 1/3 and 2/3 of the total number of linear extensions of . [11 ...
Extension of a function, defined on a larger domain; Extension of a polyhedron, in geometry; Extension of a line segment (finite) into an infinite line (e.g., extended base) Exterior algebra, Grassmann's theory of extension, in geometry; Field extension, in Galois theory; Group extension, in abstract algebra and homological algebra
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Extensibility is a measure of the ability to extend a system and the level of effort required to implement the extension. Extensions can be through the addition of new functionality or through modification of existing functionality. The principle provides for enhancements without impairing existing system functions.
A browser extension is a software module for customizing a web browser. Browsers typically allow users to install a variety of extensions, including user interface modifications, cookie management, ad blocking , and the custom scripting and styling of web pages .
Consider the two functions f and g mapping from and to natural numbers, defined as follows: To find f(n), first add 5 to n, then multiply by 2. To find g(n), first multiply n by 2, then add 10. These functions are extensionally equal; given the same input, both functions always produce the same value.
In mathematical logic, more specifically in the proof theory of first-order theories, extensions by definitions formalize the introduction of new symbols by means of a definition. For example, it is common in naive set theory to introduce a symbol ∅ {\displaystyle \emptyset } for the set that has no member.