I know many terms like function, mapping, transformation, and morphism are used for describing same mathematical object, functions. But I think that there's more explanation about these names than 'just the same'.
e.g. we use morphism when we talk about structural similarity between two structures. We use this term because we feel some 'change of shape'(but preserving some structural property).
So my question is : why do we use the term mapping? Is there any similarity between map making and defining a function?
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A (geographical) map corresponds to a one-to-one function from a region of the Earth's surface to a piece of paper.
See also Earliest Known Uses of Some of the Words of Mathematics which claims the mathematical use of "mapping" (German Abbildung) goes back to Riemann and Klein.
answered Apr 5, 2016 at 18:04