tcp_ML500 - 12/13/2005 9:28 AM
Botnst - 12/13/2005 6:18 AM
tcp_ML500 - 12/12/2005 3:16 PM
Botnst - 12/11/2005 10:49 PM
Heck, I can give an infinite (but bounded) number of coordinates on the face fo the Earth, only one of which is real. Since 1/infinite is infinite, any given coordinate is meaningless without corroboration.
PS But I AM curious.
An oversight on your part I am certain... 1/infinity tends to zero, the infinitesimal, not infinity.
The infinite but bounded universe, reduced to a spherical analogy, you are making Hawkins proud.
Take a surface as unity.
How large an area is covered by a coordinate pair? Infinitesimal.
What's the sum of the infinite number of coordinate pairs on the surface?
limit of 1/sum(infinitesimals) = 1.
I shouldn't have been so sloppy previously. Unfortunately it reveals an underlying pattern that, try as I might, defies suppression.
n/1=n has been know for a while, 1 being the identity element for multiplication, and hence, division.
I get your point, but limit of "1/sum(infinitesimals) = 1" means nothing to me, because sum(infinitesimals) means nothing to me, although the reasoning is OK, primarily because a point, in this context, does not have a measurable surface, summing an infinity of points does not make a measurable surface. Even though the surface is made of an infinity of points, the limit development is pointless as expressed.
Unless, again, we leave the realm of math to go to physics, then Plank has the answer to the definition of a minimum distance through his constant, thereby proving that the fuck from Elea was wrong, there is no paradox, motion is possible, as experienced in our daily lives.