# How to write Math statement better in limits and spacing?

Code

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\begin{equation*}
c_{0} =
\left( (u_{j})_{j \in \mathbb{N}} \subseteq \mathbb{K}
| \lim\limits_{j \to +\infty} u_{j} = 0 \, \text{ converges } \right)
\end{equation*}
\end{document}


Output

I do not like the

• unadjusted limits of lim,
• the manual spacing; I started to write \,\,\, things between things there but things get too manual fast.
• and the use of \text{...} because of printing to other formats

How can you write the statement better in limits and spacing?

• I'm not sure what you are asking. c_0 = \Bigl( (u_j)_{j\in\N} \subseteq \K \Bigm| \lim_{j\to\infty} u_j = 0 \Bigr)? – Manuel Sep 14 '15 at 10:52
• What are unadjusted limits? Where do you use \,\,\,? What is wrong with \text or what are those other formats you are talking about? I would just type \begin{equation*} c_{0} = \bigl((u_{j})_{j\in\mathbb{N}} \subseteq \mathbb{K} \bigm| \lim\limits_{j \to +\infty} u_{j} = 0 \text{ converges}\bigr) \end{equation*} and see no problem whatsoever. – LaRiFaRi Sep 14 '15 at 11:05
• Please explain the unadjusted comment. and what exaxtly is this, I do not recognize this syntax. – daleif Sep 14 '15 at 11:05
• Can you make your question more precise, it is not clear to me what you object to. Maybe you are interested in Line in set definition, How to automatically resize the vertical bar in a set comprehension? and Define pretty sets in LaTeX. This is purely mathematical nit-picking, but wouldn't one use set (curly) braces for this, and of course adding converges after one has already established the limit is 0 seems superfluous. – moewe Sep 14 '15 at 11:07

Maybe one of the following?

(The second equation, incidentally, reflects @moewe's observation that it seems redundant to require that a sequence have a (finite) limit and that it converge.)

If this isn't what you're looking for, please do clarify what you mean by terms such as "unadjusted limits" and "printing to other formats".

\documentclass{article}
\usepackage{amsmath,amssymb}
\begin{document}
\begin{equation*}
c_{0} =
\Bigl(
(u_{j})_{j \in \mathbb{N}} \subseteq \mathbb{K}
\Bigm|
\text{$\lim_{j\to+\infty} u_{j} = 0$ converges}
\Bigr)
\end{equation*}

\begin{equation*}
c_{0} =
\bigl\{
(u_{j}{)}_{j \in \mathbb{N}} \subseteq \mathbb{K}
\bigm|
\lim\nolimits_{j\to+\infty} u_{j} = 0
\bigr\}
\end{equation*}

\end{document}

• I think this is very helpful \Bigm| making the thing clearer. Thank you! – Léo Léopold Hertz 준영 Sep 14 '15 at 11:27