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Topic:
Re: E. T. Bell, Adolf Fraenkel and Ordered Pairs
Replies:
13
Last Post:
May 23, 2007 9:14 PM




Re: E. T. Bell, Adolf Fraenkel and Ordered Pairs
Posted:
May 15, 2007 3:36 PM



On May 15, 2007, at 6:16 AM, Kutler, Samuel wrote:
In any case, when I was led to teach rational numbers by starting with symbols such as (a,b) and (c,d), I called these ordered pairs, and it became clear to almost all (if not all) students quite immediately that I meant that the "a" came before the "b", and the "c" before the "d". I emphasized this by observing that in using the notation {a,b} (brackets, not parentheses) for the set consisting of a and b, no ordering is specified. In more advanced courses, I would introduce the notation {a, (a,b)} as a device for formally introducing an ordered pair without depending on geometric intuition to tell one which came first, but I took it that to do this in earlier courses would only lead to confusion.
Dear Sam, How true! And in elementary school we teach fractions (not rational numbers) as 3/4, not evan as sophisticated as a/b. The definition {a,(a,b)} is not useful for solving every day problems, but we need it to help understand Bell's difficulties. I think I once used it in finding a maximal chain with Zorn's Lemma. Peace, Don



