Re: 1-1/2+1/3-1/4+1/5-1/6+1/7

Gonçalo Rodrigues wrote:

On Tue, 12 Feb 2008 14:05:44 +0100, Han de Bruijn
<Han.deBruijn@xxxxxxxxxxxxxx> fed this fish to the penguins:

Jesse F. Hughes wrote:

G. Frege <nomail@invalid> writes:

For simplicity we assume that n, m are in N, then we can write:

x e E* <-> AnEm >= n: x e E_m,

x e E <-> EnAm >= n: x e E_m.
*
Thinking about it, I get the following criteria for the limit - if it
exists:

E = lim E_n
n
iff
x e E <-> EnAm >= n: x e E_m for all x.

With other words, x is element of the limit (if it exists) iff it is not
element _only_ of finitely many elements E_n.

Just to be clear: lim E_n = E ? n *

Or am I missing something? If I read you right, I guess I don't see
much need to discuss the lim sup and lim inf at present, since we
haven't discussed lim sup and lim inf is just another name for lim.

Surely I'm missing something.

Is mathematics the art of making things unnecessarily complicated?

http://rescomp.stanford.edu/~cheshire/EinsteinQuotes.html

"Everything should be made as simple as possible, but not simpler."
(Albert Einstein)

Please !!

Is that your pavlovian response whenever you see some mathematics that
is beyond your understanding? That it is an unnecessary complication?

Geez! In my _finitary_ comprehension, the whole thing is sooo obvious !
But that's not the game I want to play here. Therefore I'm _begging_ you
to employ a formalism which is as simple and straghtforward as possible
and not invoke unneccessary complications / generalizations or whatever.

Han de Bruijn

.

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