Re: udev and devfs - The final word

Hugo Mills
2004-01-05T18:09:47Z

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On Mon, Jan 05, 2004 at 09:52:45AM -0800, Davide Libenzi wrote:
> On Mon, 5 Jan 2004, Vojtech Pavlik wrote:
>
> > On Mon, Jan 05, 2004 at 08:13:26AM -0800, Linus Torvalds wrote:
> >
> > > But the thing is, some things you simply _cannot_ number. For example, a
> > > two-dimensional space is innumerable - you need more than one integer
> > > number to look things up. So is the set of real numbers (but not the set
> > > of fractions), etc etc.
> >
> > Two dimensional discrete space (*) is enumerable. Just start at [0,0]
> > and assign numbers going around the center in a growing spiral (**).
> > That way you assign a number to every point in that space. This is very
> > similar to the trick used to demonstrate fractions are enumerable.
>
> Vojtech, a spiral (in the math sense) won't work because whatever
> continuos function you choose for the radius, you are going to skip
> integers when the radius grows (and duplicate them when it's small). Also,
> IIRC, fractions are enumerable because they're a mapping from two
> enumerable spaces (integers): F = F(I1, I2) = I1 / I2.

I think he meant something like this:

( 0, 0)
( 1, 0)
( 0, 1)
(-1, 0)
( 0, -1)
( 2, 0)
( 1, 1)
( 0, 2)
(-1, 1)
(-2, 0)
(-1, -1)
etc.

Rationals are countable since they're the product of the integers
(numerator) and the natural numbers without zero (denominator). You
can count them in a similar way to the above "spiral", making sure
that you don't count 1/2 and 2/4 as two different numbers. :)

Hugo.

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