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

On 7 Jul., 23:31, Virgil <vir...@xxxxxxxxxxx> wrote:

The question is only this: Can removal of the removable discontinuity
yield another result than
lim_[x-->0] sinx/x = 1?

The question is, what is your justification for attempting to remove the
discontinuity in the first place?

To find the one and only true value.

For sin(x)/x the answer would be so as to have an everywhere continuous
and differentiable function.

But for your 'P(x)/K(x)', there is no justification at all, since there
is a direct way to find what the value should be "at oo".

I go the most direct way to find the value it has "at oo" - not the
value it should have.



On the other hand, the continuity of the paths guarantees that the
result is the only one possible, in mathematics.

That may be what transpires in in WM's MathUnRealism, but it does not in
actual mathematics, since by direct analysis, one can show that "at oo"
the ratio of paths to nodes must be infinite:

That argument is analog to: Contra has shown that sin0/0 = 100.
Therefore l'Hospital is wrong in this case.

Regards, WM

.