## MATHEMATICAL MAPPING

In mathematics, a mapping is a rule which relates each element *x* of one set *X* to a unique element *y* in another set *Y*. The mapping is expressed as the function, *f*, thus: *y = f(x)*. There can only be said to be a mapping from *X* to *Y* if no elements are left unmapped from *X*, and if each value of *x* is assigned to only one value of *y*.

This leads Skemp (1971, p.250) to say that geographical mapping is not a species of mathematical mapping, on the grounds that not every element in the original set *X* is represented in the image set *Y*, and that *X* cannot be well enough defined.

Cartography is then a type of mathematical modelling, necessarily involving abstraction. But it seems reasonable to argue that the original set could be defined as, say, consisting of streets, or mountains, or boundaries measured to a given tolerance.

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THE FULLER MAP

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© Paul Taylor 2001