Some thougts on cartesian products

[Christoph Zwerschke]

Bryan Olson schrieb:

>> Still think there is no such thing?
> 
> Uh, yes.
> 
>    The Cartesian product of two sets A and B (also called the
>    product set, set direct product, or cross product) is defined to
>    be the set of [...]
> 
> All sets, no strings. What were you looking at?

Not only sets. This goes on (anyway "everything is a set"). You can also 
have the Cartesian product of functions. And you can think of a string 
as a function from a countable index set I to the set of all characters 
C. So the Cartesian product of two strings will become a function from 
IxI to CxC. Since IxX is countable again, this is equivalent to a tuple 
of 2-tuples of characters which you can also interpret as a tuple of 
strings with 2 chars:

"ab" x "cd" = ("ac", "ad", "bc", "bd")

Do I have eliminated all remaining clarities now? :-)

-- Christoph