[texhax] Meaning of Code frag

Tom Schneider toms at ncifcrf.gov
Sun Feb 22 16:54:03 CET 2009


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/


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