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

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?

Regards,
G. Rodrigues
.

Relevant Pages

  • Re: Cantorian pseudomathematics
    ... lim f= f ... a function f is _nonsense_ at a iff ... In mathematics, terms which are formally defined mean only what they are defined to mean, no more and no less. ...
    (sci.math)
  • Re: Cantor Confusion
    ... convention in mathematics is a set most instructively expressed by lim ... Given a sequence of sets, S_n, what is your definition of ... standard mathematics, so it requires defining before it has meaning. ...
    (sci.math)
  • Re: Infinite series question
    ... is also known that lim ... I was looking for some good convergence of the sum ... Department of Mathematics ...
    (sci.math)
  • Re: ratio test,
    ... this that is getting me into trouble because i think when they state lim, ... because you state that the series diverges when the lim inf is greater than ... So therefore, in this example, we are perhaps looking at the lim sup here ...
    (sci.math)
  • Re: How to prove an inequality involving sequence of weighted means?
    ... Let a_n be a sequence of real numbers, ... and lim sup are quite confusing to me) ... Sdiverges and it's terms are positive, S=> oo and lim inf ...
    (sci.math)