Paul:
> [start code]
> f(x)=O(g(x))\mbox{ as }x\to a
> if and only if there exist positive numbers d and M such that
> |f(x)| \le \; M |g(x)|\mbox{ for }|x - a| < \delta.
> If g(x) is non-zero for values of x
> [end code]
>
> Is the | enclosing the functions used to denote order of growth?
It should mean the absolute value.
I tried the code chunk and it failed:
\documentclass[12pt]{article}
\begin{document}
f(x)=O(g(x))\mbox{ as }x\to a
if and only if there exist positive numbers d and M such that
|f(x)| \le \; M |g(x)|\mbox{ for }|x - a| < \delta.
If g(x) is non-zero for values of x
\end{document}
which gave:
! Missing $ inserted.
<inserted text>
$
l.3 f(x)=O(g(x))\mbox{ as }x\to
a
?
! Emergency stop.
<inserted text>
$
l.3 f(x)=O(g(x))\mbox{ as }x\to
a
No pages of output.
It's useful to give complete functional examples!
Fill in the missing $ ...
\documentclass[12pt]{article}
\begin{document}
$f(x)=O(g(x))\mbox{ as }x\to a$
if and only if there exist positive numbers d and M such that
$|f(x)| \le \; M |g(x)|\mbox{ for }|x - a| < \delta$.
If $g(x)$ is non-zero for values of $x$
\end{document}
That typesets nicely.
Looks like a snip of a $\delta-\epsilon$ proof in calculus,
not that I recall how those work anymore!
Bottom line: it is better to give complete but minimal working code
so that others can play with it.
Tom
Dr. Thomas D. Schneider
National Institutes of Health
National Cancer Institute
Center for Cancer Research Nanobiology Program
Molecular Information Theory Group
Frederick, Maryland 21702-1201
toms at ncifcrf.gov
permanent email: toms at alum.mit.edu
http://www.ccrnp.ncifcrf.gov/~toms/