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

In article <1183012452.552580.37620@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> WM <mueckenh@xxxxxxxxxxxxxxxxx> writes:
On 28 Jun., 03:12, "*** T. Winter" <***.Win...@xxxxxx> wrote:
....
> > The number of elements is *not* the sum of the elements.
>
> No. It is smaller.

Show a proof, please. First define the sum of infinitely many numbers,
and go on from there.

Sum of infinitely many natural numbers:
A sum which contains as partial sums the sum of the first n natural
numbers (definition required?) and for which holds:
If 1+2+3+...+n is defined, then 1+2+3+...+n + n+1 is defined.

This is not a definition. Or do you rule out: sum{n = 1..oo} 2n? Is
that *not* a sum of infinitely many natural numbers? But even when we
look at it as a definition of sum{n = 1..oo} n, it does not show anything
about what that sum really is. You should reconsider your ability to
provide definitions.

> If you believe that
> 1-1+1-1+1-1+-... = oo (*)
> can be defined, then it is of no use to continue this discussion at
> all. If however you can follow my arguing that this sum without any
> further definition can be restricted to
> -2 < 1-1+1-1+1-1+-... < 2

You need definition.

No, with certainty: no.

Well, as the above statement does not follow from standard definitions
and/or theorems, you need more than just stating it.

Without further definition "..." makes no sense.
Pray give a mathematical definition of that notation.

I gave a mathematical definition. But you don't know what is meant by
mathematics.

Not in the article which I reply now to, neither in another article
where you die not define it either.

> Level
>
> |0 0.
> | / \
> |1 0 1
> | / \ / \
> |2 0 1 0 1
> | /\ /\ /\ /\
> v x
>
> At height x the number of nodes is K(x) = 2^[x+1] - 1.
> At height x the number of separated path bunches is P(x) = 2^]x[.

Pray, give a definition of separated path bunch. Without definition
I can not even see the validity or invalidity of this statement.

You would also fail with a definition, I am sure.

I do not know, as I have not yet seen a consistent definition. But
clearly you are unwilling to provide definitions of the things you are
using.

> Would you agree that this result is correct although there is not a
> limit in the usual sense. Or would you prefer to say that because of
> the quotient is alternating between the epsilon surrounding of 1/2 and
> the epsilon surrounding of 1 the true result is 2^aleph_0?

Perhaps, but awaiting a definition of path bunches.

I will concentrate on discussing with sensible persons who understand
what "separated" and "path bunch" means in this case. At some point of
the regression in defining things one must stop. (I assume you also
understand this but cannot confess because then your beloved set
theory turns out as self contradictory.)

I am able to confess it. Apparently I am not sensible. And you are
unwilling, and I think even unable, to provide a definition of
"separated path bunches". Each time when I describe what I think of
what you are meaning, the only thing you state is that I am wrong.

But that is *not*
a statement about paths, but about path bunches.

Path bunches is all we have in the tree - and elsewhere.

Again in contradiction to what you wrote earlier.
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
.

Quantcast