Tony Orlow wrote: > David Marcus wrote: > > Tony Orlow wrote: > >> David Marcus wrote: > >>> Tony Orlow wrote:
> >>>> Not sure what you're asking here. It would seem that, if [0,1) contains > >>>> the same number of "points" as [0,2), then they must be smaller points, > >>>> since they accumulate half the measure. But points are considered > >>>> measureless. Personally, I think it's better to give an infinitesimal > >>>> size to a point, and say there are twice as infinitely many in [0,2) as > >>>> in [0,1). I suppose they might seem "smaller" from a distance... :) > >>> What do the quotes around "points" mean? > >> I thought I made that clear during the course of the paragraph. The > >> measures of points without measure cannot sum to any measure, so an > >> infinitesimal measure for a point, which resolves such problems, makes > >> it not exactly a point, in the standard sense. That's why I said "point". > > > > So, it isn't exactly a point, and it resolves some problem. > > Unfortunately, no one but you knows what this non-point point is. And, > > what "problem" exactly are you resolving? > > It's an infinitesimal interval and it resolves the problem of additive > measure for points.
That's nice, but you seem to have not (yet?) learned that if you use a word, it should have a definite meaning. What is an "infinitesimal interval" and what is the "problem of additive measure for points"?
