Re: equality vs. identity in Conway's "On Numbers and Games"

From: David C. Ullrich (ullrich_at_math.okstate.edu)
Date: 07/13/04 

Date: Tue, 13 Jul 2004 09:35:53 -0500

On Tue, 13 Jul 2004 08:33:11 -0400, "G. A. Edgar"
<edgar@math.ohio-state.edu.invalid> wrote:

>In article <igj7f0tmvdhjh8c1ckh5efkmrt9l5a4k0h@4ax.com>, David C.
>Ullrich <ullrich@math.okstate.edu> wrote:
>
>> On 13 Jul 2004 04:18:20 -0700, mikharakiri_nospaum@yahoo.com (Mikito
>> Harakiri) wrote:
>>
>> >On page 17 of his "On Numbers and Games" Conway writes
>> >
>> [...]
>> >
>> What's the difference between identity and equality?
>>
>
>"Equality" is a defined relation in "On Numbers and Games"
>(pages 5 and 15 of the second edition).

Oh. Thanks.

>Games x and y are identical if their left sets are identical and their
>right sets are identical. But by definition x = y means
>x >= y and y >= x, and these, in turn are defined in terms of
>>= applied to various options of x and y.

I'll have to write him a letter - "equality" and "identity" should
mean the same thing, he should call this "equality" an equivalence
relation instead, and or talk about equality ( = identity) of
the equivalence classes. I imagine he'll be completely rewriting
the next edition...<g>

>This is similar to defining the real numbers using Cauchy sequences
>of reals, and then defining "equality" of real numbers as a certain
>equivalence relation between sequences.

************************

David C. Ullrich

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