Re: ordered pair

From: Arturo Magidin (magidin_at_math.berkeley.edu)
Date: 08/31/04 

Date: Tue, 31 Aug 2004 13:35:17 +0000 (UTC)

In article <cdf67c73.0408302144.74296806@posting.google.com>,
Butch Malahide <bof@sunflower.com> wrote:
>magidin@math.berkeley.edu (Arturo Magidin) wrote in message news:<cgvsf8$2nui$1@agate.berkeley.edu>...
>> You ->could<- define ordered n-tuples "directly" the same way as you
>> do ordered pairs: the tuple (x_1,...,x_n) could be defined to be the
>> set { {x_1}, {x_1,x_2}, {x_1,x_2,x_3}, ...., {x_1,x_2,...,x_n} }; but
>> the functional point of view is more typical.
>
>Doesn't that make <a,a,b> = {{a},{a,b}} = <a,b,b>?

Yeah; I missed some parenthesis. You proceed by induction, of course,
defining (x_1,x_2) as {{x_1}, {x_1,x_2}}; then you define

(x_1,....,x_n,x_{n+1}) = ( (x_1,...,x_n),x_{n+1} )
                       = { {(x_1,...,x_n)}, {(x_1,...,x_n),x_{n+1}} }.

Thanks for catching the error. 

-- 
======================================================================
"It's not denial. I'm just very selective about
 what I accept as reality."
    --- Calvin ("Calvin and Hobbes")
======================================================================
Arturo Magidin
magidin@math.berkeley.edu

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