Re: Well Ordering the Reals


Tony Orlow wrote:
> Daryl McCullough said:
> > Tony Orlow says...
> > >
> > >David Kastrup said:
> >
> > >> How is that a "basic property"? Adding 1 to each element of a set
> > >> that has numbers in a ring is a reversible operation, so it can hardly
> > >> "imply" smaller set size. And yet adding 1 to each element of N is
> > >> _exactly_ equivalent to removing 0 from the set, without adding any
> > >> element to it.
> > >Yes, because you do not consider what happens to the set at the other end.
> >
> > On the one hand, you claim that there is no largest natural number.
> > That implies that there is no "end". So what happens at the "end"
> > is a nonsensical notion.
> >
> > Why do you keep bringing up the end of a set which you agree
> > has no end?
> >
> > --
> > Daryl McCullough
> > Ithaca, NY
> >
> >
> Because in order to measure it, you have to conceptualize some end to it, as a
> variable which can assume infinite values. I thought I said that.

Yeah, you arranged words in roughly that sequence many times. But what
does it mean, we wonder? To determine the "size" of an infinite set,
first conceptualise that it is _not_ an infinite set, then write down
the answer quick before it deconceptualises back to being infinite
again. Do you know how to catch a pink elephant?

A: nug tnahpele knip a htiw ti toohS.

And how do you catch a grey elephant then?

A: nug tnahpele knip a htiw ti toohs dna knip seog ti litnu eson sti
dloH.

Seems to me this technique might be applicable to measuring infinite
sets, somehow.
But meanwhile, we are agog to hear quite how you measure these sets of
strings that Daryl is giving you. Until you can do that, well-ordering
the reals is taking on rather a lot, I fancy.

Brian Chandler
http://imaginatorium.org

.

Relevant Pages

  • Re: Well Ordering the Reals
    ... Daryl McCullough said: ... > Tony Orlow says... ... You HAVE no definition for number of elements for infinite sets. ... > Ithaca, NY ...
    (sci.math)
  • Re: infinity
    ... >> Tony Orlow says... ... finite or infinite. ... Daryl McCullough ... Prev by Date: ...
    (sci.math)
  • Re: infinity
    ... Daryl McCullough said: ... > Tony Orlow says... ... the set is unbounded but not infinite. ... > What is the size of the set of all finite naturals? ...
    (sci.math)
  • Re: Well Ordering the Reals
    ... >> Daryl McCullough said: ... >>> Tony Orlow says... ... >> I already defined finite, infinite and infinitesimal quantities, ... It has as much to do with set sizes as your injections do with quantities. ...
    (sci.math)
  • Re: infinity
    ... > Tony Orlow wrote: ... >>Daryl McCullough said: ... > For all s a finite string, ... all lengths are finite, then none are infinite, and the language cannot be ...
    (sci.math)
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