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begin quote ita"
CHAPTER I [:] Notions from Set Theory [...] 1. SETS AND ELEMENTS. SUBSETS. "end quote
These pages assume that the reader has the book and is reading along.    
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Please read these notes from the beginning to here, and then paragraph 6 of 1.

SUBSETS

It seems to me that what Rosenlicht puts after the word 'Thus' should actually be the definition of a subset:

begin quote ita-1-1-6-pg3 "
[...] is shorthand for the statement "if   x X,   then   x Y".
"end quote

I have been using this for a long time, but it is something else that I missed on my first reading.

Exercise: The following is far more powerful than it seems. Carefully imagine in your mind, and write out on a piece of scrap paper - say on the blank side of a piece of junk mail that you are going to recycle - the quote above. But, instead of sets X and Y (in that order!), suppose that we have

(1) sets A and B;
(2) sets C and D;
(3) sets E and F;
(4) sets Y and X.

That is: Begin to see important facts in a general way. They must be expressed with particular symbols, but learn to recognize what can change without changing the fact. "The fact is the sweetest dream that labor knows." - Robert Frost, in "Mowing"

on to reading 5