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? 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. Proof by failure: Try to establish in analysis the limit oo without 1 by the sequence 0 00 000 ...
> > Your contention: This is a contradiction. You cannot get oo > with only 0's
My contention is same as before: Obviously set theory cannot reproduce the results of analysis. > > My contention: The two limits are different and there is > no contradiction.
You try to justify one error by another one. Set theory cannot reproduce mathematics. That fact is not mended by constructing another failure. But you see it better here
> > 01. > > 0.1 > > 010.1 > > 01.01 > > 0101.01 > > 010.101 > > 01010.101 > > 0101.0101 > > ... where set theory yields no digit and analysis yields inifinitely many digits left to the point.
Taking the result of set theory seriously, we get a limit less than 1. And in your example we can get rid of a 1 and have a limit oo with only zeros. Do you think to defend set theory by that arguing? Should really somebody take it seriously? And apply it anywhere? I don't believe so.