Using: Latex -> pdfLatex, and also loading another tex file written by me with:  

\input{\myPath anotherDocument.tex}
%% there is a "private" macro:
\def\foo#1{$\backslash$def$\backslash$#1$\{$the name$\}$}
%% doesn't compile without $

%% all happens before
\begin{document}


1) Why can't I define the macro JUST like others ? Because all other macros are defined without $ but also contain commands like\foo{}.
2) What does $ do ?
3) What does * do ?
4) Why do some packages influence each other ?
5) Why is the Latex syntax inconsistent ?
6) What is wrong with Latex ?


Question: Real norms on vector spaces over finite fields
Answer: The triangle inequality might allow some interesting functions, but positive homogeneity doesn't. A finite field has a prime characteristic, $p$. Positive homogeneity says $\psi(rx)=|r|\psi(x)$ for $r\in\mathbb{Q}$. To satisfy this property, $\psi(0)=\psi(px)=p\psi(x)$, which first says $\psi(0)=0$ and then $\psi(x)=0$ for all $x\in F$.