Some thougts on cartesian products

Bryan Olson fakeaddress at nowhere.org
Tue Jan 24 08:22:08 CET 2006


Christoph Zwerschke wrote:
> 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.

Snipping is not going to make the facts go away. I did not
choose the reference at issue in this strand:

     http://mathworld.wolfram.com/CartesianProduct.html

 > This goes on (anyway "everything is a set").

The claim "everything is a set" falls into the category of
'not even wrong'. Whatever semantics Python adopts, it must
be well-defined.

Watch things not be sets:

    x = [1, 1, 2]
    y = [1, 2]
    print x == y
    print set(x) == set(y)


 > 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")

I really did try to raise the real issues. I cannot make you answer,
but the question remains: are duplicate and order significant in
what you call "Cartesian product" or they not? Can you show that
your proposed language extensions are  useful and consistent in
some reasonable sense?

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

Yes. Good one. Sure.


-- 
--Bryan



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