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

In article <JKqJ9M.4Fw@xxxxxx>, "*** T. Winter" <***.Winter@xxxxxx>
wrote:

In article <1183441649.404036.29620@xxxxxxxxxxxxxxxxxxxxxxxxxxx> WM
<mueckenh@xxxxxxxxxxxxxxxxx> writes:
> On 3 Jul., 04:37, "*** T. Winter" <***.Win...@xxxxxx> wrote:
...
> > > The declaration of 0 as a natural number.
> >
> > Again, nothing more than opinion. Moreover, they are not the only ones
> > who do that.
> >
> If you can't see the facts supporting this opinion (discovery of 0
> much later than discovery of genuine natural numbers) then further
> discussion is meaningless.

So in giving names in mathematics you should consider history, otherwise
you are wrong? Sorry, in mathematics a term defines just what is given
in its definition. Nothing more, nor less. And different people give
the same name to different things.

> > Yes, especially your abuse.
>
> If you can't see the facts supporting my discovery (lim_[x --> oo]
> P(x)/K(x) in the binary tree) then further discussion is meaningless.

Yes, it is meaningless because you do not see that that limit is *not*
the necessary value.

> > > Your assertion is wrong, because an identity implies that both parts
> > > are simultaneously defined or both are undefined.
> > >
> > > SUM_[n = 1 to oo] a_n == LIM_[k --> oo] SUM_[n = 1 to k] a_n
> >
> > But in that case there *must* be a definition of the left-hand side
> > without
> > reference to the right hand side.
>
> The left hand side is an abbreviation of the right hand side.

Wrong. It is only an abbreviation of the right hand side when the right
hand side is defined.

> > But whatever, this make
> > sum{n = 1..oo} n
> > undefined because
> > lim{k -> oo} sum{n = 1..k} n
> > is undefined in ordinary mathematics. In H&J the "sum" above is *not*
> > defined using limits.
>
> SUM {n = 1..oo} n is undefined as the result of throwing dice is
> undefined in advance. Nevertheless the result cannot be negative. So
> much logic thinking should be available.
> If you can't see this fact, then further discussion is meaningless.

You are still wriggling. The sum is undefined using ordinary mathematics,
nevertheless it is possible to give a definition (so much for your
identity). Stating that something that is undefined can be compared
with something that is well-defined borders on nonsense.

Actually, it goes well beyond that border.
.

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