Re: abundance of irrationals!)

In article <IEr5A8.Evx@xxxxxx> "*** T. Winter" <***.Winter@xxxxxx> writes:
> In article <fb701d3c.0504091328.686ed77a@xxxxxxxxxxxxxxxxxx> mueckenh@xxxxxxxxxxxxxxxxx (W. Mueckenheim) writes:
....
> > You oppose to infinite sums but you need a proof for ALL n > n_0 which
> > ultimately leads to an infinite sum, before you know whether the
> > series is converging.
>
> How wrong you are. Infinite sums do *not* exist (there is no theorem
> or axiom that gives meaning to them). In the case:
> sum{k=1...n} 1/2^k = 1 - 1/2^k
> so by the *definition* of limit the series converges and its limit is 1.
> Also you do not understand Cauchy's convergence criterion. It does not
> talk about sums, but only about differences between pairs of elements.

Sorry, this is wrong (of course). It talks about differences of finite
sums.
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
.