On Nov 22, 4:54 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 22 Nov., 20:22, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > > > > > Note that I was able to handle your > > "simple" case using induction. > > > I consider the following case easy. > > If you disagree maybe you can say > > why? > > > Consider the sequence of real numbers > > > 1.0 > > 10.0 > > 100.0 > > ... > > > The limit is oo (unbounded) > > > According to set theory, the number of 1's in the limit > > is 0. (The limit of the set of positions at which we > > have a 1 is the empty set). > > Why should the 1 disappear completely?
The limit of the set of positions at which we have a 1 is the empty set. If there is a 1 it has to be a one without a position.
> But let's assume it. > > According to analysis the number of 1's in the limit is 1 and the > number of zeros left to the point is infinite.
Nonsense. There is no such thing as a number with an infinite number of zeros left of the decimal point.
According to analysis the sequence grows without bound.