FOM: ordered pair: Bourbaki Vedasystem at
Mon May 3 19:22:29 EDT 1999

In a message dated 5/3/99 2:01:10 PM Eastern Daylight Time, 
kanovei at writes:

>  Could you please explain how the rotten set theoretic 
>  pair definition <x,y>={{x},{x,y}}, possibly even with 
>  silly theorems like your favourite one above, 
>  can make any harm to *the modern programming
>  languages like Java, C++, Eiffel* ? 

Of course it cannot make any harm (as well as any use)
to programming languages.
My point was that using abstract data types one can hide
there concrete implementations so irrelevant facts cannot appear
(see my answer to Martin Davis).

The Bourbaki's definition of ordered pair also "hides" its concrete 
implementation, however, they use {x, {x, y}} to prove the consistency 
of their definition.

Victor Makarov

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