Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
- From: tommy1729 <tommy1729@xxxxxxxxx>
- Date: Wed, 16 Jan 2008 17:48:44 EST
hagman wrote :
On 16 Jan., 21:56, tommy1729 <tommy1...@xxxxxxxxx>
wrote:
1-1/2+1/3-1/4+1/5-1/6+ ....
this series can be made to sum to anything.
No, *this* series converges to one and only one
value.
However, the convergence is not absolute, so we can
find
*another* converging series for any given target
value;
then this latter series is related to the one above
by having the
same summands in a different order - but order is
important
for a series (a series is *not* a sum)
true , but thats exactly what i mean.
hotel
apparently most of you dont understand hilbert's
question :
however you dare too claim that i dont !!
but you are the one confused !
if you understand so well answer this simple
N = [0,1,2,3,4,5,...]
Apparently you want to talk about a sequence, not the
mere set?
"Square" elements.
"Square" = [0,1,4,9,16,25,36,...]
notice the " point to point correspondance "
now the set containing N but not "Square" is L
rearrange the set N : containing both L and
called T.
this set contains all non-negative integers and is
count oo long for the squares and thus the limit of
T = [0,1,4,9,16,25,...,2,3,5,6,7,8,10,...]
now since the "one to one correspondance" we can
our series can skip the non-square elements.
Indeed this is indexed by a different ordinal (2
omega) of the same
cardinality.
yes , in terms of set theory yes.
but i wanted to avoid another discussion about set theory so i avoided the word cardinality.
position does 2 occur in the set T ?
still dont believe it ?
than answer the simply question : at what finite
Sets do not specify positions for their elements. The
position of 2 is
of course omega,
then comes 3 at omega+1 etc.
not true ;
ordered sets do have specific positions for their elements.
admit i am correct.
if you answer oo ; thats not finite , and thus you
omega is not precisely the same as oo.
like i said i wanted to avoid a set theory discussion, it is indeed omega as you say.
...
else im curious what number you will come up with
its another series "skipping elements" method ,
as for Riemann's series theorem : just admit it ;
similar and justified by Hilbert's hotel.
value of a series , since if you dont , there is
"skipping elements" is the only way to choose any
divergence as in :
actually different series.
1-1+1-1+1-1+...
or you use analytic continuations which are
or you hide the skipping in a subtle multisection.
the principle is so simple.
you are confused ; not me.
afterall , you seem to have understud my argument , sorry for the sloppy language and the avoiding of set theory lingo.
regards
tommy1729
.
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