READING: I §2 6
Back to reading:
I §2 5
begin quote ita"
CHAPTER I [:] Notions from Set Theory [...] §2. OPERATIONS ON SETS. "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 10 (on ordered pairs) of §2.
I note that, in the first part of the paragraph on ordered pairs, Rosenlicht introduces the ordered pair informally - in the same way that I did in the spoken reals. In the latter part of the paragraph, a set theoretic definition is given, , where the three-lined equals sign means that what is on the left is equal by definition to what is on the right.
This definition does precisely what we want: to any two objects a, b (distinct or not) it assigns an object (a,b), and it does this in such a fashion that
I would like quickly to verify this. Using the definition of set equality, we need to show that