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begin quote ita"
CHAPTER I [:] Notions from Set Theory [...] 3. FUNCTIONS. "end quote
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DEFINITION:   f : XY

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:

begin quote ita-1-3-4-pg8 "
[...] 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   XY   with the property that for any   xX   there is one and only one   yY   such that   (x,y)   is in the subset. If the function is denoted   f:XY   then the unique   y   referred to above is, of course,   f(x).
"end quote

on to reading 4