**READING: I §3 3**
Back to reading**:**
I §3 2

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*CHAPTER I* [:]
**
Notions from Set Theory
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These pages assume that the reader has the book and is reading along. topic index contents

Please read these notes from the beginning to here, and then paragraph 4 of §3.

In the cartesian product, every element of the first set is paired with every element of the second set. In a function from one set to another, every element of the first set is paired with one and only one element of the second set. Hence the definition:

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ita-1-3-4-pg8
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[...] it is easy to define the notion of function in terms of more primitive concepts of set theory, as follows: If *X* and *Y* are sets, a function from *X* into *Y* is a subset of *X**Y* with the property that for any *x**X* there is one and only one *y**Y* such that (*x,y*) is in the subset. If the function is denoted *f***:***X**Y* then the unique *y* referred to above is, of course, *f*(*x*).

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