[texhax] Meaning of Code frag
P. R. Stanley
prstanley at ntlworld.com
Sun Feb 22 16:58:46 CET 2009
>It's a code frag taken from the Wikipedia page on the Big O notation:
http://en.wikipedia.org/wiki/Big_O_notation
>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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