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

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 Don Cook Posts: 101 Registered: 12/3/04
Re: E. T. Bell, Adolf Fraenkel and Ordered Pairs
Posted: May 15, 2007 3:36 PM
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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

Date Subject Author
5/12/07 James T. Smith
5/12/07 Don Cook
5/14/07 Robert (Bob) Eldon Taylor
5/14/07 Gordon Fisher
5/18/07 Robert (Bob) Eldon Taylor
5/21/07 Gordon Fisher
5/15/07 Kutler, Samuel
5/15/07 Don Cook
5/15/07 Gordon Fisher
5/19/07 Franz Gnaedinger
5/21/07 Milo Gardner
5/21/07 Gordon Fisher
5/22/07 Don Cook
5/23/07 Milo Gardner