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

In article <1183710371.727433.25080@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
WM <mueckenh@xxxxxxxxxxxxxxxxx> wrote:

On 6 Jul., 04:08, "*** T. Winter" <***.Win...@xxxxxx> wrote:
In article <1183441649.404036.29...@xxxxxxxxxxxxxxxxxxxxxxxxxxx> WM
<mueck...@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.

The name is at least part of the definition because all definitions
consist of words many of which are names for notions. So it would make
mathematics unnecessary complicated if every name meant the opposite
of its usual meaning.

Every definition has a context in which it is to hold, and outside that
context it may have different meanings, or none.

Otherwise there would only be one language on Earth.

> > 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.

The limit is not necessary the value, but for continuous functions it
is. lim [x-->o] sinx/x = 1 unless you define another value at x = 0
and by that make the function discontinuous.

WRONG! The function defined merely by f(x) = sin(x)/x is not even
defined at x = 0 unless and addition to that definition is appended to
extend the definition to cover x = 0.

At least in standard mathematics. What goes on in WM's MAthUNRealism is
quite often different from standard mathematics.



The paths of the tree are
continuous, however.

That is an entirely different form of 'continuity' than the continuity
of a real function at a real point. And neither type holds "at oo".




Therefore the limit P(x)/K(x) is the only
possible choice.

Non-existence of a value "at oo" is the standard choice unless one does
some form of compactification to allow even the possibility of
continuity "at oo" to be considered.

WM's MathUnrealism is as odd as a Klein bottle on steroids.
.