The Virgin Birth of Points
in [Physics]
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From: Lester Zick on 11 Nov 2007 16:40 The Virgin Birth of Points ~v~~ The Jesuit heresy maintains points have zero length but are not of zero length and if you don't believe that you haven't examined the argument closely enough. ~v~~
From: William Elliot on 11 Nov 2007 23:57 On Sun, 11 Nov 2007, Lester Zick wrote: > The Virgin Birth of Points > ~v~~ > > The Jesuit heresy maintains points have zero length but are not of > zero length and if you don't believe that you haven't examined the > argument closely enough. > Clearly points don't have zero length, they have a positive infinitesimal length for which zero is just the closest real approximation.
From: Robert J. Kolker on 12 Nov 2007 06:46 Lester Zick wrote: > The Virgin Birth of Points > ~v~~ > > The Jesuit heresy maintains points have zero length but are not of > zero length and if you don't believe that you haven't examined the > argument closely enough. In Euclidean space a set which has exactly one pont as a member has measure zero. But you can take the union of an uncountable set of such singleton sets and get a set with non-zero measure. Bob Kolker
From: Robert J. Kolker on 12 Nov 2007 06:48 William Elliot wrote: > > Clearly points don't have zero length, they have a positive infinitesimal > length for which zero is just the closest real approximation. You don't need to resort to non-standard analysis. Within the realm of standard real numbers, the matter is settle using measure (either Borel or Lebesque) Bob Kolker
From: David C. Ullrich on 12 Nov 2007 07:02
On Sun, 11 Nov 2007 20:57:47 -0800, William Elliot <marsh(a)hevanet.remove.com> wrote: >On Sun, 11 Nov 2007, Lester Zick wrote: > >> The Virgin Birth of Points >> ~v~~ >> >> The Jesuit heresy maintains points have zero length but are not of >> zero length and if you don't believe that you haven't examined the >> argument closely enough. >> >Clearly points don't have zero length, they have a positive infinitesimal >length for which zero is just the closest real approximation. Erm, no. Points (or rather singletons) have zero length. ************************ David C. Ullrich |