"Jim Callahan" <magicjim@islc.net> wrote:
> OK you can map the infinite but at what point do you finish?
Depends on what you mean by finish. If you map the infinite unto the
Riemann Sphere via the Stereographic Projection, you always "finish" at the
north pole.
In my previous example of mapping the integers into the
interval [0, 1] of reals, it's not so much a matter of finishing as
deciding that the finish actually occurs inside the interval.[1] One of
the most astonishing results of Cantor's work was to show that even all the
"rational" numbers (of the form m/n for m, n integers) only compose a
*countable* infinity, and are thus *Vastly* outnumbered by the irrational
numbers.
> Does infinite space exist? Not for those who cannot grasp the
> concept. ......Jim
Last I heard, the universe too was finite... even if you can grasp the
concept, that don't make it reality.
ERiC
[1] For instance, one can map them via f(x) = 1/x, for x non negative
integer. It's trivially obvious to see that such a mapping maps the
countable integers into the interval (0, 1], and thus
into [0, 1]