Re: Orlow cardinality question

Tony Orlow (aeo6) wrote:
> Randy Poe said:
> >
> >
> > Tony Orlow (aeo6) wrote:
> > > Yes, I claim the the set you define as having all finite values has no distinct
> > > upper bound, as you folks keep emphasizing when you ask for a largest finite
> > > number, and yet you claim it is infinite. This set doesn't really exist.
> >
> > The phrase "and yet" sounds like you see a problem
> > here, in declaring that a set "has no upper bound"
> > and "is infinite". (Note on blurred terminology:
> > the SET is infinite, the ELEMENTS have no upper
> > bound. "Upper bound" is not a property of a set).
> >
> > Why do you feel that being infinite is incompatible
> > with having no upper bound on the elements?
> >
> > - Randy
> >

I just want to label part of a sentence so forgive me breaking up your
quote...

> I don't. The problem is the asusmption that all the members are finite in
> value, as I've said a million times, since ...

(1) ... no infinite number of values
differing by a constant finite value can fit in a finite range of
value.

Let's call this Tony's claim (1).


Of course your claim (1) is true, and no-one disagrees with it. But
what does it mean? Simply that the unbounded set of pofnats, formed
from zero and any (finite, but unlimited) number of additions of 1
thereto, which is plainly not a set of a finite size, since it can't be
counted with a ditty that stops, cannot fit in a finite range of
values. What's the problem? Actually no problem at all, except that you
are following your intuition from experience of finite sets. This
intuition says that supposing you lay the elements of a set out in a
line, as the pofnats can be in an obvious way, them if you want to find
the "range of values", you can find the ends by moving out until there
are no more elements; you can then "shrink" this range so that it
exactly fits, from the leftmost element to the rightmost element. The
distance between these two endpoints is exactly the range of the
values. All this works fine for finite sets; it also works for infinite
set *****IF THE ENDPOINTS EXIST*******. But if an endpoint does not
exist, it cannot be used to measure the range.

Well, you've been shown this before, over and over again. The pofnats
do not have an endpoint at the right. There is therefore no
contradiction whatsoever in the fact that all of the elements of the
pofnats, not being the rightmost point, are finite. All you need to do
is to think about this carefully and seriously, with your finite-based
preconceptions turned off.

Brian Chandler
http://imaginatorium.org

.

Relevant Pages

  • Re: Cantor and the binary tree
    ... >> Tony Orlow (aeo6) wrote: ... > important properties of relative size when it came to infinite sets. ... precise means of discriminating between finite and infinite". ...
    (sci.math)
  • Re: infinity
    ... Tony Orlow (aeo6) wrote: ... >infinite value, then I am only taking a finite number of steps. ... Prev by Date: ...
    (sci.math)
  • Re: infinity
    ... >> Tony Orlow (aeo6) wrote: ... >>> ever be infinite, so the maximum difference in the set is some finite value. ... >> Uh, so if you're counting these natural numbers with a ditty, the ...
    (sci.math)
  • Re: Epistemology 201: The Science of Science
    ... In sci.math Tony Orlow (aeo6) wrote: ... :> In sci.math Wolf Kirchmeir wrote: ... :> by an infinite number of 1's, but this is not an integer. ...
    (sci.cognitive)
  • Re: Epistemology 201: The Science of Science
    ... In sci.math Tony Orlow (aeo6) wrote: ... :> In sci.math Wolf Kirchmeir wrote: ... :> by an infinite number of 1's, but this is not an integer. ...
    (sci.physics)
Quantcast