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I've written this code

\subsection*{Definitie 1}
\textit{Als $z$, $f(z)$ \in \mathbb{R}^{m}, dan is de M-de Frechet afgeleide van $f$, voorgesteld
door $f$^{(M)}$(z)$ een operator op \mathbb{R}^{m} \times \mathbb{R}^{m} \times \ldots \times \mathbb{R}^{m} (M maal)
, die lineair is in elk van de operandi met als waarde}

But I can't compile the document, as I get a "$ missing" and "Undefined control sequence" error. I've already checked this code a dozen times, but can't seem to find anything wrong. Any ideas?

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4  
Welcome-to-tex-sx! Have a look at the Not so short guide to LaTeX, and in your first few documents, always build up your code slowly, compiling frequently- this will help you find where the errors are :) –  cmhughes Nov 26 '12 at 16:54
    
@cmhughes very appropriate advise. Do you mind if I rephrase it (well copy it almost verbatim) into my answer? –  Gonzalo Medina Nov 26 '12 at 17:12
    
@GonzaloMedina sure, go for it :) –  cmhughes Nov 26 '12 at 17:15
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2 Answers

You had several math mode expressions written in text mode; I've fixed them in the code below. I would suggest you to use the amsthm package to define a theorem-like structure with the desired formatting for your definitions; in this way, the formatting and numbering are dona automatically:

\documentclass{article}
\usepackage{amssymb}
\usepackage{amsthm}

\newtheoremstyle{mydefi}
  {\topskip}{\topskip}
  {\itshape}{}
  {\bfseries}{}
  {\newline}{}
\theoremstyle{mydefi}
\newtheorem{defi}{Definitie}

\begin{document}

\begin{defi}
Als $z$, $f(z) \in \mathbb{R}^{m}$, dan is de $M$-de Fr\'echet afgeleide van $f$, voorgesteld door $f^{(M)}(z)$ een operator op $\mathbb{R}^{m} \times \mathbb{R}^{m} \times \cdots \times \mathbb{R}^{m}$ ($M$ maal), die lineair is in elk van de operandi met als waarde
\end{defi}

\end{document}

enter image description here

I used Fr\'echet; but loading inputenc with the appropriate encoding, you can simply write Fréchet.

By the way, for definitions it's also common to use use the roman (upright) font instead of italics; in this case, you can change the definition of the mydefi style to:

\newtheoremstyle{mydefi}
  {\topskip}{\topskip}
  {}{}
  {\bfseries}{}
  {\newline}{}

I would also like to suggest you (quoting cmhughes's valuable comment) to have a look at some introductory material (the Not so short guide to LaTeX (available in seveal languages) and the amsmath package documentation, for example); in your first few documents, always build up your code slowly, compiling frequently- this will help you find where the errors are.

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3  
Congrats on reaching 100K :-) –  Harish Kumar Nov 26 '12 at 17:02
    
May I suggest (again) to change Frechet to Fr\'echet (or Fréchet + proper inputenc) and \ldots to \dotsb? And congratulations on the 100k! –  kahen Nov 26 '12 at 17:02
    
@HarishKumar thank you very much! –  Gonzalo Medina Nov 26 '12 at 17:02
    
@kahen of course, will do the changes right now; thanks for pointing them out. And thanks for your kind words! –  Gonzalo Medina Nov 26 '12 at 17:03
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You have few misplaced and missing $s:

\documentclass{article}
\usepackage{amsmath,amsfonts}
\begin{document}
\subsection*{Definitie 1}
\textit{Als $z$, $f(z) \in \mathbb{R}^{m}$, dan is de M-de Frechet afgeleide van $f$, voorgesteld
door $f^{(M)}(z)$ een operator op $\mathbb{R}^{m} \times \mathbb{R}^{m} \times \ldots \times \mathbb{R}^{m}$ (M maal)
, die lineair is in elk van de operandi met als waarde}
\end{document}
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Thank you! I thought that only characters were to be placed between the $'s. And I was using the wrong math package. (I'm just learning :s ) –  viraxis Nov 26 '12 at 16:53
1  
Further problems are: (1) missing $..$ pairs around "M", (2) Fréchet's name is misspelled, (3) \ldots in the product should be \dotsb and (4) this would probably be better implemented using amsthm, ntheorem or thmtools. –  kahen Nov 26 '12 at 16:54
1  
@kahen: I don't understand anything written in there ;-). Is it german? Only goal is to eliminate errors. :-) –  Harish Kumar Nov 26 '12 at 16:58
1  
@HarishKumar it's Dutch probably. –  kahen Nov 26 '12 at 16:59
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