Does Python need a '>>>' operator?

Andrew Dalke dalke at dalkescientific.com
Tue Apr 16 01:30:27 EDT 2002


Aahz:
>What's a co-finite set"?  (Yeah, I could Google for it, but I usually
>understand *your* explanations -- eventually. ;-)

I'm not my Uncle Timmy, but I can give it a go.  Let me dust off
my math degree, as soon as I can find the sucker...

It's a set whose complement (that is, the set containing everything
which isn't in the original set) is finite.

For example, in integers the set

  ...-3, -2, -1, 0, 1, 3, 4, 5, 6, 7, ...
                     ^^^ 2 is missing

is cofinite because its complement, which is {2}, is finite.

The set of even integers is not a cofinite subset of the integers
because its complements, the odd integers, is also infinite.

They are relevant here because bits can only be constructed either
explicitly (you need to say them) or though operators.  Operators
like 'and' and 'or' don't make infinite sets, but 'not' does.
This value cannot be represented directly as an infinite set of
bits, but can be represented as a finite set of bits and a flag
that says "use the complement."  There is no way to construct
a bitlist using these operators (in finite time) which is not
either finite or cofinite, which means there is a relatively
easy way to store these calculations on a computer.

                    Andrew
                    dalke at dalkescientific.com






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