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

On 10 Jul., 22:40, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <1184096254.060347.302...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,

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.

The simple truth is that SUM(1/2^n) can be proven to be not larger
than 1. Further it can be proven, in marthematics (neglecting
MatheRealism), that every value less than 1 can be surpassed. That
makes SUM(1/2^n) = 1 (and in MatheRealism SUM(1/2^n) =< 1 is also a
valuable result).

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.

To have an infinite value describes nothing but the fact that every
given value is surpassed. There is no other kind of infinity.

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.

It has an upper and a lower bound. Therefore it can be used for
calculations. With S = 1-1+1-1+1-+.... we can state, mathematically,
10*S < SUM(1/n) and related expressions.



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,

Your technology is nothing but a perverted game of gamblers, not more
valuable than "counter strike" and related blossoms of a degenerating
society.

Regards, WM

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