CHAPTER 1 |
Sets and Functions |

This chapter introduces two major notions: sets and functions. We are all familiar with real functions, for example, *f* (*x*) = 2*x* + 1 and *g*(*x*) = sin(*x*). Here the approach is somewhat different. The first difference is that we do not limit the discussion to the set of real numbers; instead, we consider arbitrary sets and are mostly interested in sets that contain only a finite number of elements. The second difference is that we do not define a “rule” for assigning a value for each *x*; instead, a function is simply a list of pairs (*x*, *y*), where *y* denotes the value of the function when the argument equals *x*. The definition of functions relies on the definitions of sets and relations over sets. That is why we need ...

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