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

G. Frege wrote:

On Mon, 16 Jul 2007 15:08:25 +0200, Han de Bruijn
<Han.deBruijn@xxxxxxxxxxxxxx> wrote:

But I'm fascinated by the fact that there exist NO other shapes of the
sin(x)/x rather than the sinc(x) function in the real (physical) world.
Only _this_ one is relevant:

sinc(x) = sin(x)/x for x <> 0
= 1 for x = 0

And I'm asking the community to explain this (not by coincidence) fact.

It's just that this is the ONLY possible extension of x |-> sin(x)/x
from (the domain) IR\{0} to IR such that the resulting function is
continuous (and even differentiable) on (all of) IR.

You know, there's an old saying "Natura non facit saltus" ("nature
does not make (sudden) jumps"), though I'm in doubt if this statement
can still be considered to be true in the light of modern quantum
mechanics.

See:
http://en.wikipedia.org/wiki/Natura_non_facit_saltus

How about "physical" functions which are defined at a closed interval of
real numbers? Are they always continuous there? What do you think?

Han de Bruijn

.

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