Difference between revisions of "Function"
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* [[Function/Introduction | Introduction to Functions]] | * [[Function/Introduction | Introduction to Functions]] | ||
* [[Function/Intermediate | Intermediate Functions]] | * [[Function/Intermediate | Intermediate Functions]] | ||
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− | + | == History of Functions == | |
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− | ==History of | ||
Without being used explicitly, the notion of function first appears with the ancient Greeks and Egyptians. | Without being used explicitly, the notion of function first appears with the ancient Greeks and Egyptians. | ||
Revision as of 00:43, 15 July 2006
This article is a stub. Help us out by expanding it.
A function is a rule that maps one set of values to another set of values. For instance, one function may map 1 to 1, 2 to 4, 3 to 9, 4 to 16, and so on. This function has the rule that it takes its input value, and squares it to get an output value. Let's call this function . A common notation to define
is:
. This tells us that
is a function that squares its argument (its input value). Note that this "rule" can be arbitrarily complicated and doesn't need to be given by a simple formula or description. The only requirement is that
should be uniquely determined by
. The following are examples of functions:
for
, otherwise
Since functions cover such an enormous part of mathematics, we divide this topic into several articles:
History of Functions
Without being used explicitly, the notion of function first appears with the ancient Greeks and Egyptians.
The rigorous definition was stated in the 19th century and is the result of the works of some famous mathematicians: A.L. Cauchy, L. Euler, B. Riemann. With the development of set theory, a new branch of mathematics appeared, mathematical analysis, in which the notion of function has a central role.