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

On 22 Jun., 23:35, Franziska Neugebauer <Franziska-
Neugeba...@xxxxxxxxxxxxxxxxxxx> wrote:

I recently denied that

sum_{n e N} 1/2^n

can be attached a value of 5, because it is already defined by the
standard definition to be

sum{n in N} (1/2^n) := lim sum_{i = 0}^n (1/2^i) = 2
n->oo

while

sum_{i e N} i

is not defined by the standard limit definition and hence a value can be
attached to it consistently.

It has been already defined by the standard definition that no real
value can be attached to sum_{i e N} i. We orthodox mathematicians
looked for any real number such that we could apply Cauchy's standard
procedure, which, as you may know, can even be applied without knowing
the number in advance, well, even without such a number existing. By
this orthodox standard procedure we could prove that there is no real
number which could be the sum_{i e N} i. Is test of Cauchy-convergence
a standard and orthodox-enough procedure for you?

Therefore the range has been extended, in orthodox mathematics and
without any asterisked lim*-symbol, such that, again in orthodox
mathematics and without any asterisked lim*-symbol, the limit is oo.
As oo =/= 0, this is a contradiction like 5 =/= 1.

That, dear Franziska Blee, is orthodox mathematics.

Regards, WM

.

Relevant Pages

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    ... On 23 Jun., 13:37, Franziska Neugebauer <Franziska- ... This statement of yours is usually called a "contradictio in adjecto". ... addressed by the term "authorities of orthodox mathematics". ... real limit may be chosen arbitrarily and, after having done so, may ...
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