Re: infinity

In article <MPG.1d613f09e3c5f417989fe0@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:

> > If you do that then you
> > are rearrangeing the numbers in the infinite series.


> That really shouldn't matter for infinite series, given the
> communtative nature of addition.

TO obviously does not understand the distinction between
(1) absolute convergence and (2) conditional convergence
for "infinite" series.

Commutativity of addition can proved to hold for finite sums from the
definitions and axioms of the various number systems.

It can be PROVED to hold also for absolutely convergent series, but it
can also be proved NOT to hold for conditionally convergent series.

Proof, as usual, trumps intuition, particularly an intuition as
misleading as TO's.
.