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Possible Duplicate:
Is there any difference between mapping and function?

I am an aspiring mathematician who just started out. What is the difference between a function and a map? Or are these notions equivalent?

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    See this [question](http://math.stackexchange.com/questions/95741/is-there-any-difference-between-mapping-and-function). It is identical.2012-12-10
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    I doubt there is even a precise definition of a function, because any definition has a counterexample.2012-12-10
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    @glebovg, "function" has a precise definition: A function from a set $A$ to a set $B$ is a subset $f$ of $A \times B$ such that for any $a \in A$ there exists a unique $b \in B$ such that $(a,b) \in f$. In this notation, you would denote $b$ by $f(a)$ and the point is that a function is completely determined by its graph.2012-12-10

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