READING: I §3 8
Back to reading:
I §3 7
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 sentences 4 and 5 of paragraph 7 of §3.
THE IDENTITY FUNCTION
An example of a function that is one-one onto is, for any set X, the identity function i : XX, given by i(x) = x for all xX. (Note that what goes under the name "the function x" in elementary calculus is actually the identity function on the set of real numbers.)
The parenthetical remark assumes Rosenlicht's prerequisites. Given the description of the identity function however, the parenthetical remark makes sense even without prior knowledge of the 'real' numbers.