On 17 Dez., 16:43, calvin <cri...@windstream.net> wrote: > On Dec 17, 2:07 am, netzweltler <reinhard_fisc...@arcor.de> wrote: > > > On 17 Dez., 07:28, calvin <cri...@windstream.net> wrote: > > > > Imagine counting all positive integers over > > > a unit period of time, from zero to one, thusly: > > > Count 1 at time 1/2, 2 at time 3/4, 3 at > > > time 7/8, and so on, with each integer coming > > > at half of the remaining time after the last > > > integer counted. As the time moves inexorably > > > toward one, and becomes almost one, the number > > > of integers counted becomes just as almost infinite. > > > For t<1 is valid, the number of integers counted is finite. So, almost > > infinite = finite, right? > > Eight, but I was trying to be funny, changing > 'almost' from a quantifier to a time-oriented > meaning.
Nevertheless, your thought experiment makes sense to me. To be more correct: For _each_ t<1 is valid, the number of integers counted is finite.
We have infinitely many integers counted before t = 1. Even if we cannot apply an "almost infinite" count.