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

On 12 Jul., 01:52, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <1afb1$46948483$82a1e228$10...@xxxxxxxxxxxxxxxx>,
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&;
http://groups.google.nl/group/sci.math/msg/5f901fb48c959010?hl=nl&;
http://groups.google.nl/group/sci.math/msg/00e4e198d9d92c40?hl=nl&;
http://groups.google.nl/group/sci.math/msg/5cdf3ee484117124?hl=nl&;

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

Han de Bruijn

There are two similar functions, one of which is not even defined at x =
0 and another which is continuous, and even differentiable, there.-

And there are uncountably many others with f(x) = r in R. But only one
of these functions exists in useful mathematics. And f(x) for this one
can be determined by l'Hospital.

Regards, WM

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