When a zero isn't zero (math quote)
Dave L. Renfro
but a google-web search gives only 2 hits (both being
the same book) and a google-book search gives only
7 hits (5 essentially different items, one of which
is the google-web hit I got):
"A zero of order zero is a regular point at which the
function is not zero."
I saw this in Pi Mu Epsilon Journal [Volume 2, Number 5
(Fall 1956), p. 224], where it's followed with "(From a
book on complex variables.)" From the google-book hits
it appears the original source is Volume 1 of Knopp's
"Theory of Functions".
Dave L. Renfro
Tonico
Indeed. It is a foot note in page 90 in the 1st american edition of
Knopp's book, 1945.
Tonio
Remcheese
"Dave L. Renfro" <renf...@cmich.edu> wrote in message
news:013e6bed-5af1-4c32...@w19g2000yqk.googlegroups.com...
That book is a 9 on my sale of 1 to 10 where 10 is the hardist.
excellent book complex functions, quite difficult, beyond advanced calculus
only 142 pages of 4in by 6in pages in vol 1
came out in 1945,
Dover has reprinted it, so it is low cost now.
basic theory of functions of one complex variable, at a pace that will
allow for the inclusion of some non-elementary topics at the end. Basic
Theory: Holomorphic and harmonic functions; conformal mappings; Cauchy's
Theorem and consequences; Taylor and Laurent series; singularities;
residues; Dirichlet Series such as the Riemann Zeta Function
Remcheese
"Tonico" <Toni...@yahoo.com> wrote in message
news:b9a7111f-815d-4dad...@m16g2000yqc.googlegroups.com...
Tonio
The entire footnote says;
" If f(z) is regular at Zo and f(Zo) not equal to a, it is often convenient
to call the pont Zo an a-point of order zero. A zero of order zero is a
regular point at which the function is not zero."
and it is under
Definition. A point Zo of a region of regularity of the function f(Z) is
called a zero of the function if f(Zo) = 0. In general, if f(Zo) = a, Zo is
called an a-point of f(Z).
[read Zo as Z sub zero)
David C. Ullrich
<renf...@cmich.edu> wrote:
>O-K, this may be a well-known folklore math quote,
>but a google-web search gives only 2 hits (both being
>the same book) and a google-book search gives only
>7 hits (5 essentially different items, one of which
>is the google-web hit I got):
>
>"A zero of order zero is a regular point at which the
>function is not zero."
Heh.
The definition also occurs in an exercise in Complex Made
Simple, not in those words.
Anyway, an excellent reason to buy the book is that you _can_
find the phrase "non-zero zeroes" there...
>I saw this in Pi Mu Epsilon Journal [Volume 2, Number 5
>(Fall 1956), p. 224], where it's followed with "(From a
>book on complex variables.)" From the google-book hits
>it appears the original source is Volume 1 of Knopp's
>"Theory of Functions".
>
>Dave L. Renfro
David C. Ullrich
"Understanding Godel isn't about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)