Re: Cantor and the binary tree



Tony Orlow (aeo6) wrote:

> > TO keeps assuming that to have infinitely many of something requires the
> > "distance" between them to be infinitely large. This is a false
> > assumption.
> It is true when the distance between neighbors is finite and constant. If you
> measure paths in units of branches, and say they are infinitely long, then that
> means they have infinitely many branches.

Of course it is so. If you have infinitely many meters, then this makes
up an infinite distance.
But do not try to convince set theorists. With respect to the magnitude
of numbers they refer to potential infinity. With respect to the number
of numbers they point to actual infinity.
Of course either both is actually infinite or both is not.

Regards, WM

.

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: Orlow cardinality question
    ... >> Tony Orlow (aeo6) wrote: ... and yet you claim it is infinite. ... Simply that the unbounded set of pofnats, ...
    (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)