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:
“Why does man freeze to death trying to reach the North Pole? Why does man drive himself to suffer the steam and heat of the Amazon? Why does he stagger his mind with the mathematics of the sky? Once the question mark has arisen in the human brain the answer must be found, if it takes a hundred years. A thousand years.”
—Walter Reisch (1903–1963)