is the base-13 number

which (in base-10) equals

Every other polynomial maps to a unique integer in the same way. One small problem remains. The preimage of the mapping isn’t the whole set of integers, so what we know right now, is that the cardinality, of the set of polynomials, is less than or equal to the cardinality of the set of integers. No problem. The set of all zero-degree polynomials is a subset of all polynomials, and all zero-degree polynomials maps to a single integer and all integers is mapped by a single zero-degree polynomial. This implies that the cardinality of the set of all polynomials is greater than or equal to the cardinality of the set of integers.

The only possibility that remains is that the cardinality of the polynomials and the integers is exactly equal. Technically we need to show that the integers is countable, by mapping them 1-1 to the natural numbers, but that is trivial.

"*p

does the job.

$  xmodmap -pk | less

When you have found the keycode and the keysym you just enter

$ xmodmap -e 'keycode <keycode> = <keysym>'

and then the key is remapped.

EDIT 08-04-2011:
Use the command xev to find the keycode for the key you want to remap. If I want to change the key that is the half fraction on my Lenovo I type in

$ xmodmap -e 'keycode 49=dollar'

tar cvzf archivename.tar.gz foldernametotar

Udpak arkiv med

tar xvzf archivename.tar.gz

from __future__ import decision

det kunne være pænt sejt hvis det virkede…

function menu($items, $id, $show_submenus) {
    return render_partial('menu', array(
        'items' => $items,
        'id' => $id,
        'show_submenus' => $show_submenus
    ));
}

Repetitionen er rimelig tydelig, men jeg vil gerne have funktionen “menu” så jeg i min template kan skrive

<div class="some_wrapper">
    <?=menu($items, 'mainmenu', true)?>
</div>

istedet for

<div class="some_wrapper">
    <?=render_partial('menu', array('items'=>$items, 'id'=>'mainmenu', 'show_submenus'=>true)?>
</div>

Løsningen er en php-funktion jeg har overset indtil i dag. Compact tager et vilkårligt antal strenge. For hver streng undersøger den om der er en variabel med samme navn defineret i samme scope, som compact bliver kaldt. Hvis der er, bliver variablens værdi tilføjet til det array compact i sidste ende returnerer. Arrayet compact returnerer har variablens navn som key og variablens værdi som value. Lige hvad der skal bruges til at gøre min menu-funktion pænere.

function menu($items, $id, $show_submenus) {
    return render_partial('menu', compact('items','id','show_submenus'));
}

\makeatletter
\renewcommand*\env@matrix[1][*\c@MaxMatrixCols c]{%
  \hskip -\arraycolsep
  \let\@ifnextchar\new@ifnextchar
  \array{#1}}
\makeatother

og vupti så kan man få lodrette streger ved at angive en ekstra parameter til matrix-environmentet.

\begin{bmatrix}[ccc|cc]
    2 & 1 & 2 & 1 & 0 \\
    1 & 2 & 3 & 0 & 1
\end{bmatrix}