Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
- From: G. Frege <nomail@invalid>
- Date: Tue, 12 Feb 2008 21:42:19 +0100
On Tue, 12 Feb 2008 14:58:43 +0100, Han de Bruijn
<Han.deBruijn@xxxxxxxxxxxxxx> wrote:
That does not suffice in mathematics.
Geez! In my _finitary_ comprehension, the whole thing is sooo obvious !
PLEEEZE note:
(1) "Confusion in math can be avoided by stating clear definitions
(first) and (then) formulating proofs _based on that definitions_."
(G. Frege)
(2) "Unproven statements carry little weight in the world of
mathematics." (Amir D. Aczel)
It seems that you've already forgotten what I've said in one of my posts
Therefore I'm _begging_ you to employ a formalism which is as simple
and straightforward as possible
(*sigh*):
"WARNING: It seems to me that you are lacking some prerequisites for
this discussion. Hence the following might not be clear at all. Now YOU
have to be patient."
Now concerning the notion of /limit/ for sequences of sets, there
actually IS a simple formalism. (But do develop that formalism one has
to refer to the basic DEFINITIONs mentioned in my other post).
Anyway here is a simple formalism concerning limit for sequences of
sets:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let (E_n) be a sequence of sets.
Let
oo oo oo oo
A = UNION SECT E_m, B = SECT UNION E_m.
n=1 m=n n=1 m=n
(UNION... the set theoretic union, SECT... the set theoretic
intersection.)
If
A = B,
then the limit of (E_n) exists, and we have
lim E_n = A = B.
n
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
A simple and clean approach. Remember:
"Everything should be made as simple as possible, but not simpler."
(Albert Einstein) ^^^^^^^^^^^^^^^
F.
--
E-mail: info<at>simple-line<dot>de
.
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