# Mathematics Prelims

## July 14, 2008

### A Note on Notation

Filed under: About — cjohnson @ 1:06 pm

For the moment I’m just going to be writing straight up LaTeX in my posts because I don’t want to take the time to generate images of everything.  (If you know of an easy solution though, let me know!)  There are a few custom aliases I use for things that I write over and over again, so here they are.

\def\R{\mathbb{R}}      % The reals
\def\N{\mathbb{N}}      % The naturals
\def\Q{\mathbb{Q}}      % The rationals
\def\C{\mathbb{C}}      % The complex plane
\def\M{\mathcal{M}}     % Measurable sets
\def\B{\mathcal{B}}     % Borel sets
\def\O{\mathcal{O}}     % Open sets
\def\F{\mathcal{F}}     % A sigma algebra F
\def\Fx{\mathcal{F}_X}  % Sigma algebra F generated by random var. X
\def\A{\mathscr{A}}     % Script A
\def\W{\Omega}          % Capital omega
\def\w{\omega}          % Lowercase omega
\def\L{\mathscr{L}}     % Lebesgue-integrable functions
\def\esssup{\text{ess sup}}  % Essential supremum
\def\iff{\Leftrightarrow}    % If and only if
\def\implies{\Rightarrow}    % Implies
\def\e{\epsilon}             % Epsilon
\def\d{\delta}               % Delta

Update Thanks for all the comments about how to put LaTeX code in WordPress!  I’ll fix the existing posts this morning and will be sure to use that in upcoming posts too.

1. WordPress supports latex, for instance $e^{i\pi}=-1$. All you do is that you put the word ‘latex’ immediately after the first dollar sign. Edit this post to see the example.

Comment by Charles — July 15, 2008 @ 12:33 am

2. You’re on WordPress. Just wrap it in $latex (drop the space) to begin and$ to end. For example:

$\mathbb{R}$

Comment by John Armstrong — July 15, 2008 @ 1:20 am

3. http://thewe.net/tex/
the tool is helpful to see the LaTex format online,but these fomulas must be put between [; and ;]

Comment by BearXu — July 15, 2008 @ 1:45 am

4. Comment by A. G. — July 15, 2008 @ 2:09 am

$\mathbb{R}\qquad$ The reals
$\mathbb{N}\qquad$ The naturals
$\mathbb{Q}\qquad$ The rationals
$\mathbb{C}\qquad$ The complex plane
$\mathcal{M}\qquad$ Measurable sets
$\mathcal{B}\qquad$ Borel sets
$\mathcal{O}\qquad$ Open sets
$\mathcal{F}\qquad$ A sigma algebra F
$\mathcal{F}_X\qquad$ Sigma algebra F generated by random var. X
$\mathscr{A}\qquad$ Script A
$\Omega\qquad$ Capital omega
$\omega\qquad$ Lowercase omega
$\mathscr{L}\qquad$ Lebesgue-integrable functions
$\text{ess sup}\qquad$ Essential supremum
$\Leftrightarrow\qquad$ If and only if
$\Rightarrow\qquad$ Implies
$\epsilon\qquad$ Epsilon
$\delta\qquad$ Delta
if you don’t use \def
\def\R{\mathbb{R}} % The reals
I’ve written
with an opening $and a closing$ before latex and \qquad

Comment by Américo Tavares — July 15, 2008 @ 7:43 am

6. I’ve written
with an opening $and a closing$ before latex and after \qquad

Comment by Américo Tavares — July 15, 2008 @ 7:50 am

7. To insert space you could use “latex \qquad” (with $before and after it). I’ve corrected to $\mathbb{R}$ $\qquad$ The reals $\mathbb{N}$ $\qquad$ The naturals To display greater symbols in sums, fractions, etc. you can use “\displaystyle” $\displaystyle\sum_{n=1}^{\infty}|a_nb_n|=\displaystyle\sum_{n=1}^{\infty}\dfrac{|x_ny_n|}{\displaystyle\sum_{n=1}^{\infty}\left(|x_n|^p\right)^{1/p}+\displaystyle\sum_{n=1}^{\infty}\left(|y_n|^q\right)^{1/q}}\le 1$ Comment by Américo Tavares — July 15, 2008 @ 2:37 pm 8. Ah, thank you very much for the hint! I was wondering if there was some way to do that earlier! Comment by cjohnson — July 15, 2008 @ 2:41 pm 9. To insert space you could use “latex \qquad” (with$ before and after it). I’ve corrected to
$\mathbb{R}$ $\qquad$ The reals
$\mathbb{N}$ $\qquad$ The naturals

To display greater symbols in sums, fractions, etc. you can use “\displaystyle”

$\displaystyle\sum_{n=1}^{\infty}|a_nb_n|=\displaystyle\sum_{n=1}^{\infty}\dfrac{|x_ny_n|}{\left(\displaystyle\sum_{n=1}^{\infty}|x_n|^p\right)^{1/p}+\left(\displaystyle\sum_{n=1}^{\infty}|y_n|^q\right)^{1/q}}\le 1$

Comment by Américo Tavares — July 15, 2008 @ 2:50 pm

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