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

In article <1184148654.059994.123760@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
WM <mueckenh@xxxxxxxxxxxxxxxxx> wrote:

On 10 Jul., 22:44, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <1184096471.659205.71...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,

WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:
On 9 Jul., 21:56, Virgil <vir...@xxxxxxxxxxx> wrote:

Then according to WM, every derivative must always equal 1 at all
points, and f(x) = |x| must have a derivative at x = 0, and lots
more.

That's nonsense.

Maybe, but it is WM's nonsense, not mine, to argue that functions must
continuous at points outside their domains.

Continuous functions must be continuous.

No function is continuous at any point outside its domain of definition,
however continuous it may be within that domain.

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.

The function sin(x)/x does not care a damn about your judgement
whether it is defined or not at x = 0. It is defined there since 1696
when l'Hospital wrote his book.

If you are trying to say that l'Hospital claimed any more about value of
sin(x)/x "at 0" other than that the limit of sin(x)/x, as x approached
0, equals 1, you are wrong.

Or is it better style to say that it does not give two hoots about
your defining it?

My computer knows that sin(x)/x is not defined at x = 0.
Even my calulator knows it. But then, my calculators knows a good deal
more of mathematics than WM does.
.