Re: ** says: Definition: sum{i in N} i = 0

On 3 Jul., 04:32, "*** T. Winter" <***.Win...@xxxxxx> wrote:
In article <1183010035.373819.18...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> WM <mueck...@xxxxxxxxxxxxxxxxx> writes:
> On 27 Jun., 22:51, Franziska Neugebauer <Franziska- > Neugeba...@xxxxxxxxxxxxxxxxxxx> wrote:

> > WM wrote:
> > > I prefer to give he following proof of
> > > -2 < 1-1+1-1+1-1+-... < 2.
> >
> > Can you rephrase "1-1+1-1+1-1+-..." without using "..." in order to
> > clarify what you understand by "..."?
> >
> There is a set of sums each of which contains 1 and contains X - 1 + 1
> if it contains X. (*)

So sums are strings of symbols. This set does *not* contain the string
"1 - 1 + 1 - 1 + 1 - 1 + 1 ...", because all strings in this set are of
finite length.

In particular because there are no other options. My result -2 <
1-1+1-1+1-1+-... < 2 olds for any string of this kind. But IF there
were an infinite string, then my result would also cover it.

Similar to N: The infinite string N is nothing but the union of all
finite strings {1,2,3,...n}.

> My sum is the smallest one of them. What is smallest? My sum does not
> contain terms which are not immediately necessary to satisfy my
> requirement (*).

And this makes no sense.

Correct. An infinite set makes no sense. I agree completely. But if an
infinite set is assumed to make sense, then it is the limit of
infinitely many finite sets, each of which obeys logical laws.

Similar to the paths of the tree. They are nothing but the union of
finite paths.

Regards, WM


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