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

In article <1184151023.224193.137430@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
WM <mueckenh@xxxxxxxxxxxxxxxxx> wrote:

On 11 Jul., 12:26, hagman <goo...@xxxxxxxxxxxxx> wrote:
On 11 Jul., 11:44, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:





On 11 Jul., 09:19, Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> wrote:

Virgil wrote:
In article <1184096471.659205.71...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:

The derivative of |x| is not

continuous but -1 for negative x and +1 for positive x. In contrast
sinx/x is continuous. Your example fails.

The expression sin(x)/x is not even defined for x = 0, so that WM is
claiming that it has a value when it does not have a value.

Ah, My old friend the SINC-function:

http://groups.google.nl/group/sci.math/msg/c83b58832ecdff3f?hl=nl&htt...

It IS defined for x = 0 and its value IS always 1 at x = 0 .

Of course. Only by decoupling mathematics from any meaningful and
valuable science and destroying it into pieces as a useless and
worthless game for gamblers, this conclusion can be avoided.

By the way, Cantor, the great icon of many of these gamblers, thought
quite different. But they who know so little, also don't know that.

Cantor's second these defended at his habilitation was: Iure Spinoza
mathesi (Eth. pars. I. prop. XXXVI, app.) eam vim tribuit, ut
hominibus norma et regula veri in omnibus rebus indagandi sit. My
translation: Spinoza is correct in assigning mathematics the power to
be norm and guide line for recognizing the truth in all respects.

To find the true value of sinx/x at x = 0 is a splendid example of
this power.

Regards, WM

Then why don't you accept what that norm and guide line
says, namely that sinx/x is not defined at x=0 even though
there exists exactly one function R->R that is continuous
throughout and coincides with sinx/x on R\{0}?

Because this is *not* the norm and guide line.

It is outside of WM's MathUnRealism.

The formulatory precision is certainly one of the points
that make it attractive to view math as a "norm and guide
line for recognizing the truth"

This kind of "formulatory precision" is just the opposite of
recognizing the truth.

And in WM's MathUnRealism, black is often white and white black.





By taking the plunge to accept the actual infinite (without any
"formulatory precision" but simply stating: "there exists a set ...")
mathematics has been perverted, i.e., now we are forced to accept such
silly things as SUM(N) = 0, because otherwise the "the exists" would
be contradicted

WM's non-sequiturs have reached a new high here.

BTW, what is the undoubtedly true value of
exp(-1/x^2) at x=0?
Mathematicians, when following their norm and guide line
will be cautious to answer this - what about you?

Not everything has an undoubtedly true value. Already 0^0 = 1 needs
definition. But sinx/x has one and only one true value at x = 0.

WM swallows camels and strains at gnats if he can say that 0^0 needs any
more definition than 0/0.

Regards, WM
.

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