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Topic: ? 417 An implication of actual infinity
Replies: 2   Last Post: Jan 17, 2014 3:46 PM

 Virgil Posts: 8,833 Registered: 1/6/11
Re: ? 417 An implication of actual infinity
Posted: Jan 17, 2014 3:46 PM

mueckenh@rz.fh-augsburg.de wrote:
> On Friday, 17 January 2014 16:59:23 UTC+1, wpih...@gmail.com wrote:
> > On Friday, January 17, 2014 8:54:19 AM UTC-4, muec...@rz.fh-augsburg.de
> > wrote:

> > > On Tuesday, 14 January 2014 23:14:55 UTC+1, wpih...@gmail.com wrote:
> > > > > I am not considering the limit
> > > > So you are not considering an infinite sum.
> > > If there are infinitely many natural numbers, then I am considering
> > > infinitely many finite sums.

> > And, by definition, the infinite sum is the limit of
> > the infinitely many finite sums. So if you do not consider
> > the limit you do not consider the infinite sum.

> There is no infinite sum but, as you say, only the limit. This limit has no
> definition by infinitely many numbers, because in mathematics, never
> infinitely many numbers can be listed number by number.

A sequence of positive real numbers whose partial sums are collectively
bounded,, will have a limit sum, regardless of whether WM has any finite
definition for such a sum or not.

Or does WM claim a "real number system" in which there are of sets of
rationals bounded above that need not have any least upper bound?

WM's systems are sufficiently strange that he might just claim that.
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