On Wed, 31 Jan 2007 03:54:47 +0900, toshiaki wrote:
> "Dave Seaman" <email@example.com> wrote in message > news:firstname.lastname@example.org... >> What is this line you are talking about? Evidently it does not contain > all the >> reals, but you don't way which ones are included.
> Metric space or measure space defined by computable numbers.
So you are using "line" to mean something other than R, or a real interval.
>> > As for plane filling curve, does it pass trough un computable number > too?
>> It passes through all all points in the unit square, whether the >> coordinates are computable or not.
> I think that one to one correspondence from a line to the other line of > different lengh, is that between computable numbers. Can uncomputable number > in a line be projected to a point in the other line from a pole?
That would be "line" in the standard sense, not the sense in which you are using the word.
A space-filling curve is a surjection f: [0,1] -> [0,1]^2. Notice that the domain includes noncomputable numbers, and the codomain includes points with noncomputable coordinates.