READING: I §3 3
Back to reading:
I §3 2
begin quote ita"
CHAPTER I [:] Notions from Set Theory [...] §3. FUNCTIONS. "end quote
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.
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:
[...] 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).