David Marcus wrote: > 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"? >
