On Tue, 8 Jan 2002, Tomasz Wegrzanowski wrote:
> On Mon, Jan 07, 2002 at 11:47:29AM -0500, Mathieu Bouchard wrote:
> > On Fri, 4 Jan 2002, Tomasz Wegrzanowski wrote:
> > I think you're better off defining a measure... well I don't know, but I
> > wouldn't think of a problem space as continuous enough to warrant defining
> > a density. The question would be "what is your total interest in this set
> > of problems", that is, a power(Problems) -> R_{0+} function, such that it
> > is homomorphic under addition (set addition is union presuming mutually
> > exclusive sets), and M(x)+M(not x) = M(everything)...
> Problem space is at least dense, as you need dense set to
> represent some of requirements that are part of your problem,
> like all performance-related issues.

Well, if a problem, to be solvable, has to be of finite length in a finite
alphabet, then the problem space is discrete, even though it's
theoretically infinite. If you think about real numbers that can be
incorporated in the problem definition: the subset of the real numbers
that can actually be written down (in whatever form) is countable. It's
"bigger" than the Rational set just like the latter is "bigger" than the
Integer set, but it's still countable.

> Well, interest density is function of what you are likely to actually
> do, not what you would like to do. This function diverges only if you
> have too ambitious plans, and it has good meaning in that case - you
> aren't going to finish them.

This would explain a lot about my projects... ;-)

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Mathieu Bouchard                   http://hostname.2y.net/~matju