How We Understand Mathematics by Jacek Woźny

Author:Jacek Woźny
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

4.6 Definition by Graph, the Small Spatial Story of a Hiker

Defining a mapping as a set of ordered pairs is sometimes referred to as “definition by graph.” This is how Herstein introduces it:Let us motivate a little the definition that we will make. The point of view we take is to consider the mapping to be defined by its “graph.” We illustrate this with the familiar example y = x2 defined on the real numbers S and taking its values also in S. For this set S, S x S, the set of all pairs (a, b) can be viewed as the plane, the pair (a, b) corresponding to the point whose coordinates are a and b, respectively.1 In this plane we single out all those points whose coordinates are of the form (x, x2) and call this set of points the graph of y = x2.

(Herstein 1975: 10)

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