Re: Peano's space-filling curve

From: John Morgan (john.morgan_at_REMOVECAPSataraxie.fr)
Date: 06/07/04 

Date: Mon, 7 Jun 2004 14:17:58 +0200

David C. Ullrich <ullrich@math.okstate.edu> wrote in message
news:fa16c0dm9nh04mpb4ra1c89q00did2mrd1@4ax.com...
> On Sat, 5 Jun 2004 19:40:36 +0000 (UTC), Dave Seaman
> <dseaman@no.such.host> wrote:
>
> >On Sat, 05 Jun 2004 13:53:18 -0500, David C Ullrich
wrote:
> >> On Sat, 5 Jun 2004 13:50:34 +0200, "John Morgan"
> >><john.morgan@REMOVECAPSataraxie.fr> wrote:
> >
> >>> I have a problem applying "onto" for the Peano
> >>> construct. If the line passes arbitrarily close to
> >>> a point, so that all neighbourhoods of that point
> >>> contain point(s) through which the line passes,
> >>> does that make it "onto".
> >
> >> No. To be onto it has to actually pass through
> >> every point. Which it does.
> >
> >Actually, since f is continuous, f([0,1]) is compact and
> > therefore closed. Hence, the fact that f([0,1]) is
dense
> > in [0,1]^2 is a sufficient condition for f to be onto.
>
> We all understand that. Well, most of us do - in a context
> where one of us is having so much trouble.
> understanding simple definitions

If you mean me , why don't you write "John Morgan". After
all, I think I have explained sufficiently often for you to
know it by now, that I am not one of you.

Here I read that f is continuous and onto. Elsewhere a
poster tells me that f cannot be all three of '1 to
1',continuous and onto. So f is not '1 to 1'? Re-arrange the
following words to make a well-known phrase, or saying.
"together., Get, act, your,"

> (as evidenced by _repeated_ confusion over how I and I^2
> can have the same cardinality even though space-filling
> curves are not bijections) it seems like pointing this out
> is going to cause more confusion than claification.

After reading the post, the response, and the response to
the response, I think I can see more clearly than ever why I
am experiencing confusion. If the numerous clever people on
this group had discussed the problem of explaining Peano to
a non-mathy before setting out to do so, they might have
saved all of us a lot of time and headaches. I still only
have part of the picture, a full three and a half weeks and
a certain amount of rancour later

Cheers,

John

Relevant Pages

  • Re: Peanos space-filling curve
    ... most of us do - in a context ... why don't you write "John Morgan". ... After reading the post, the response, and the response to ... am experiencing confusion. ...
    (sci.fractals)
  • Re: Turing Machines and Physical Computation
    ... citing once again (although without their original context for reasons ... controls ate all pellets delivered. ... Stemmer and some other psychologists treat under the ... response to one stimulation and penalized for the same ...
    (comp.theory)
  • Re: Turing Machines and Physical Computation
    ... citing once again (although without their original context for reasons ... controls ate all pellets delivered. ... Stemmer and some other psychologists treat under the ... response to one stimulation and penalized for the same ...
    (sci.math)
  • Re: Turing Machines and Physical Computation
    ... >> take their emotional responses as something to further act upon. ... I have commented on what i got from each in this context. ... >> response to one stimulation and penalized for the same ... >> free to internalize in his peculiar neural way. ...
    (comp.theory)
  • Re: Turing Machines and Physical Computation
    ... >> take their emotional responses as something to further act upon. ... I have commented on what i got from each in this context. ... >> response to one stimulation and penalized for the same ... >> free to internalize in his peculiar neural way. ...
    (sci.math)