READING: I §1 4
Back to reading:
I §1 3
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. topic index contents
Please read these notes from the beginning to here, and then paragraph 6 of §1.
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".
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"