# How can I make text inside set notation look like normal text?

I'm very new to LaTeX, and have never been very good with computers, so apologies for not knowing how to post questions on here properly or missing out anything important.

I have this:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
$F_f=\{z\in \mathbb{\hat{C}}:(\vert f^n(z) \vert) is bounded\}$
\end{document}

"is bounded" comes out in italics and I'd like it to look like normal text (as in text not in  or  signs. Any help would be appreciated.

And I realize that I've got lots of \ signs missing, they don't seem to show up.

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Use: \text{ is bounded}. –  Gonzalo Medina Mar 23 '14 at 16:56
Use \text{ is bounded} and be happy. –  Sigur Mar 23 '14 at 16:56
Better yet, \{z\in\hat{\mathbb{C}}:\text{$(\lvert f^n(z)\rvert)$ is bounded}\} –  egreg Mar 23 '14 at 16:58
Wow, that's great! Thank you! –  kingzapper Mar 23 '14 at 17:00
@egreg You should make that an answer. –  Andrew Swann Jan 18 at 13:48

I'm not fond of long set descriptions like this, so I'll show also how I'd describe the set.

The trick is to temporarily go in text mode. However the input

(\lvert f^n(z) \rvert) \text{ is bounded}\}

is awkward and I find it much better to use \text for the whole description, getting back in math mode inside it.

\documentclass{article}
\usepackage{amsmath,amssymb}

\begin{document}
Define
$F_{f}=\{z\in \hat{\mathbb{C}}: \text{(\lvert f^n(z) \rvert) is bounded}\}$

We define $F_{f}$ as the set of $z\in\hat{\mathbb{C}}$ such that the
sequence $(\lvert f^n(z) \rvert)$ is bounded.
\end{document}

Note that the correct syntax is \hat{\mathbb{C}} and it would be meaningful to have something like

\newcommand{\numberset}[1]{\mathbb{#1}}
\newcommand{\nC}{\numberset{C}}
\newcommand{\hnC}{\hat{\nC}}

so we can write z\in\hnC and don't bother with formatting instructions in the document body.

Note also that \lvert...\rvert is the correct usage when amsmath is loaded.

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Now that you are at it, I think it would also be great \DeclarePairedDelimiter\set{\lbrace}{\rbrace} and \DeclarePairedDelimiter\abs{\lvert}{\rvert} and use them appropriately. –  Manuel Jan 18 at 14:10
@Manuel I don't agree about \set; for \abs it could be. However it's outside the scope of the question. –  egreg Jan 18 at 14:19
@egreg Is there a particular reason for writing, say, $\text{f is}$ instead of $f\text{ is}$? (Personally I like your way of doing is, so I'm just curious.) –  Svend Tveskæg Jan 18 at 15:07
@SvendTveskæg I find it awkward to have f\text{ is...}: \text{$f$ is...} is clearer and there's no risk of forgetting spaces. The clause is the complete $f$ is.... –  egreg Jan 18 at 15:09
@SvendTveskæg Under normal settings, no. –  egreg Jan 18 at 15:11