**READING: I §2 6**
Back to reading**:**
I §2 5

*begin quote ita***"**

*CHAPTER I* [:]
**
Notions from Set Theory
**

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.

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begin quote
ita-1-2-10-pg7
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**"**

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

For the left hand direction of the double arrow, we use the equalities

For the right hand direction of the double arrow, we must show that the assumption of equality between the sets implies the equalities on the right hand side of the double arrow. If the sets are equal, then each element of one must be an element of the other. This shows first that