Mathematics
In mathematics, the 'extension' of a mathematical concept is the set that is specified by that concept.
For example, the extension of a function is a set of ordered pairs that pair up the arguments and values of the function; in other words, the function's graph. The extension of an object in abstract algebra, such as a group, is the underlying set of the object. The extension of a set is the set itself. That a set can capture the notion of the extension of anything is the idea behind the axiom of extensionality in axiomatic set theory.
This kind of extension is used so constantly in contemporary mathematics based on set theory that it can be called an implicit assumption. It can mean different things in different cases, and there is no universal definition of the term "extension".
Read more about this topic: Extension (semantics)
Famous quotes containing the word mathematics:
“In mathematics he was greater
Than Tycho Brahe, or Erra Pater:
For he, by geometric scale,
Could take the size of pots of ale;
Resolve, by sines and tangents straight,
If bread and butter wanted weight;
And wisely tell what hour o’ th’ day
The clock doth strike, by algebra.”
—Samuel Butler (1612–1680)