Re: Compression test on permutations

erpy <info@xxxxxxxxxxxxxxxx> wrote:

That's why I'm saying that zero is conveniently saw one way or the other
(i.e. as "no numbers" or as the number Zero).
If you have only the number zero, the product of zero "items" with zero
"items" is zero obviously, 0*0 = 0.

If you care about my two cents: I do not like both explanations. IMHO,
the best way to justify this convention is to look at the analytic
continuation of the faculty, namely the gamma function:

x! = Gamma(x+1) = \int_0^\infinity t^x exp(-t) dt

and you get from that 0! = Gamma(1) = 1 (by simply computing the integral).

And, by that you also find, as has already been argued, that (-1)! =
1/0, and indeed the gamma function has a simple pole at 0, (and so on
all other negative integers).

So long,
Thomas
.

Relevant Pages

  • Re: Fourier Transform challenge
    ... and the gamma function is analytic only in the right half plane. ... I had also forgotten that the Gamma function is analytic everywhere except at the negative integers. ... Start by integrating only over the interval. ... the limit exists and is zero by the Riemann-Lebesgue Lemma (see ...
    (comp.dsp)
  • Re: Question on pole-zero cancellation
    ... The numerator includes a zero at DC, the denominator gives a pole at DC, ... no matter how the factor 1 is represented, provided the representation ... By factoring out the poles and zeros that cancel before we implement ...
    (comp.dsp)
  • Re: Poles an Zeros
    ... I have never heard of any confrontation occurring between the Polish air ... force and a Japanese Zero. ... the Zero would have defeated the Pole. ... Need to learn how to apply control theory in your embedded system? ...
    (sci.electronics.basics)
  • Re: Question on pole-zero cancellation
    ... The numerator includes a zero at DC, the denominator gives a pole at DC, ... and so these cancel, ... Pole-zero cancellations work if the mathematics is exact. ...
    (comp.dsp)
  • Re: pole zero stuff
    ... > I am confused about pole - zero diagrams and how they relate to filter ... Imagine that the plane is covered flat with an elastic sheet. ... location of each pole. ... axis in the s-plane or the unit circle in the z-plane. ...
    (comp.dsp)