READING:     I     3     10                    Back to reading:     I     3     9
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 8 of 3.

THE IMAGE OF A SET UNDER A FUNCTION

begin quote ita-1-3-8-pg10 "
If   f : XY   is a function and   X X,   then the subset of   Y   given by


f ( X ) = { f (x) : xX }
[...]
is called the image of   X under   f,   or simply the image of   X ,   if there is no danger of confusion.
"end quote



There is always danger of confusion when I am the reader, but this seems clear enough.

Now, after you read the next quote, replace the   x   by   a,   let   aX,   and read the equation again without the   "for each"   part.



begin quote ita-1-3-7-pg10 "
The two uses we have made for the symbol   f ( ) are related by the equation


f ( { x } ) = { f (x) }   for each   xX .
"end quote

on to reading 11