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

In article <1184096254.060347.302660@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
WM <mueckenh@xxxxxxxxxxxxxxxxx> wrote:

On 9 Jul., 21:37, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <1183966290.591477.221...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,

WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:
On 9 Jul., 00:05, Virgil <vir...@xxxxxxxxxxx> wrote:

***'s premise was not that SUM(N) cannot be defined in R

Whether it was his premise or not: SUM(N) cannot be defined in R, at
least in mathematics.

That claim begs the question. While it is quite true that the series
does not converge, it is only a matter of convention that one speaks of
the value rather than the limit of convergent series, so that,
technically, NO series has a value, though some of them have limits.

Many series have real values, one of them is SUM(1/2^n).

They converge to real values, but unless Wm claims that one can ACTUALLY
come to an end in an infinite addition, which violates his own
assumptions, there can be no /value/ to such a sum, merely a limit to
the partial sums.


Many series
have infinite values, one of the is SUM(1/n), another one is SUM(n).

They do not have "infinite values", they lack limit values, which is
quite a different thing.

Many series have no values, one of them is 1-1+1-1+1-+....
(nevertheless one can give bounds).

That one has as much of a "value" as any infinite series, i.e., none at
all.

In some of your crazy axiom systems, this may be
different.

Finite series have values. Some infinite series have limits, but none of
them, technically, have values.

You adhere to the wrong technology.

My "technology" is quite correct mathematically, however it may appear
in WM's MathUnRalism.

Regards, WM
.

Quantcast