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88 CHAPTER 4 Some Mathematical Topics on Which to Practice Proof Techniques of the function. If f is the letter representing the correspondence, then we use the notation f : A B to indicate that f is a correspondence from A to B. If x A, then f (x) indicates the element of B that f associ- ates to x, and it is called the image of x under f. The definition of function is deceptively easy, but it is full of details. A correspondence must meet two requirements to be a function. The image of every element of A must exist. The image has to be well defined in B. There can be only one element of B selected to be the image of a given element of A. f A B x f(x)