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

On 6 Jun., 20:05, Franziska Neugebauer <Franziska-
Neugeba...@xxxxxxxxxxxxxxxxxxx> wrote:
WM wrote:

SUM{n>0}1/n is not less than 1.
Nicole d'Oresme proved this and even the unboundedless of the
harmonic series, i.e., the sum of unit fractions.

Even if it was the Pope your rise up against ***'s definition is
of no avail.

It was only a Bishop (of Lisieux). But what counts more: He was a
mathematician.

To experts your maneuver is known by the name "appeal to authority".
The problem is thathttp://pt.wikipedia.org/wiki/Nicole_d'Oresme
most likely never proved sum{i in N} i =/= 0 hence the reference
to him is futile.

I was not present when he (or not he?) proved the divergence of the
harmonic series. But I know this proof is correct.

So you admit that he did _not_ prove sum{i in N} i =/= 0? Fine.

AFIK Nicole d'Oresme was the first one to prove the divergence of the
harmonic series. I think I read it in Moritz Cantor's great historical
books. But I am not sure and too lazy to look it up.

If you doubt, however, then attend one of my lectures. I myself prove
it at least twice every year.


But in its more general meaning, as positive infinity, it proves
the sum > 1.

1. How do you know that H&J do _not_ mean the "special meaning" of
aleph_0? The wish was father of the thought?

For the record: You don't know.

2. Can you give proof by quote that H&J meant (the naive) "positive
infinity" when they wrote "aleph_0"?

They prove that aleph_0 is larger than any natural number, in
particular they prove that aleph_0 is larger than 0.

Look up the meaning of "quote", please!

Look up the meaning of lazy, please. If you are interested in their
proof, look it up yourself.

Regards, WM

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