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i(x) = x is another function that does nothing to x. So i(1) = 1, i(2) = 2, and so on. This is called the '''identity function'''.

i(x) = x is another function that does nothing to x. So i(1) = 1, i(2) = 2, and so on. This is called the '''identity function'''.

Some functions do not have numbers as outputs. For example, we can define a function "pres" that takes a number n, and returns the name of the nth [[President_of_the_United_States_of_America| American President]]. So, pres(1) = [[George Washington]] (the first president), pres(2) = [[John Adams]] (the second president), and so on.

Some functions do not have numbers as outputs. For example, we can define a function "pres" that takes a number n, and returns the name of the nth [[President of the United States of America|American President]]. So, pres(1) = [[George Washington]] (the first president), pres(2) = [[John Adams]] (the second president), and so on.

Similarly, not all functions take numbers as inputs. For example, we could define a function "presnumber" that takes the name of an American President (the nth in sequence), and outputs n. Thus presnumber(George Washington) = 1, presnumber(John Adams) = 2. This would be the inverse of pres defined above.  (However, due to a historical curiosity, this function is not properly defined; see below.)

Similarly, not all functions take numbers as inputs. For example, we could define a function "presnumber" that takes the name of an American President (the nth in sequence), and outputs n. Thus presnumber(George Washington) = 1, presnumber(John Adams) = 2. This would be the inverse of pres defined above.  (However, due to a historical curiosity, this function is not properly defined; see below.)

There are functions that take objects other than numbers as inputs. For example, rotation can be thought of as a function that takes a shape as an input, and outputs that shape rotated by a certain angle.

There are functions that take objects other than numbers as inputs. For example, rotation can be thought of as a function that takes a shape as an input, and outputs that shape rotated by a certain angle.

==External Link==

==External links==

*[http://mathworld.wolfram.com/Function.html Function -- from Wolfram MathWorld]

*[http://mathworld.wolfram.com/Function.html Function -- from Wolfram MathWorld]

[[category:mathematics]]

[[Category:Mathematics]]