Re: Is continuum completely filled up?

On Thu, 1 Feb 2007 04:46:57 +0900, toshiaki wrote:

"Dave Seaman" <dseaman@xxxxxxxxxxxx> wrote in message
news:epobdt$q9m$1@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx

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.

Yes, I am talking about traditional theory.
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.

As Arturo Magidin has pointed out, I neglected to say that it's a
*continuous* surjection.

It is constructed with map from Cantor set to [0,1]^2. I have overlooked
this.

Me too. That's understandable, since the domain is all of [0,1].

But note that even the Cantor set, being uncountable, necessarily
includes uncomputable numbers.




--
Dave Seaman
U.S. Court of Appeals to review three issues
concerning case of Mumia Abu-Jamal.
<http://www.mumia2000.org/>
.

Relevant Pages

  • Re: Is continuum completely filled up?
    ... different lengh, ... That would be "line" in the standard sense, not the sense in which you ... points with noncomputable coordinates. ... U.S. Court of Appeals to review three issues ...
    (sci.math)
  • Re: Is continuum completely filled up?
    ... different lengh, ... That would be "line" in the standard sense, not the sense in which you ... points with noncomputable coordinates. ... Ozaki Tosiaki ...
    (sci.math)