Best typesetting of formula

My personal motto is if I have a clear message to convey, it's better to make it obvious

\documentclass{article}
\usepackage{amsmath,array}
\usepackage{xcolor,cancel}

\newcommand*\mathsetfont{\mathbf}
\newcommand*\DeclareMathSet[1]{%
  \expandafter\newcommand\csname set#1\endcsname{\mathsetfont{#1}}
}
\DeclareMathSet{N}
\DeclareMathSet{Q}

\begin{document}

\[
\left\{
\begin{array}{c@{,}c@{,}c@{,}c@{,}}
\ldots         &\ldots         &\frac{1983}{4} &\cancel{\textcolor{red}{\frac{1984}{4}}}\\[1ex]
\frac{1985}{4} &\frac{1986}{4} &\frac{1987}{4} &\cancel{\textcolor{red}{\frac{1988}{4}}}\\[1ex]
\frac{1989}{4} &\frac{1990}{4} &\frac{1991}{4} &\cancel{\textcolor{red}{\frac{1992}{4}}}\\[1ex]
\frac{1993}{4} &\frac{1994}{4} &\frac{1995}{4} &\cancel{\textcolor{red}{\frac{1996}{4}}}\\[1ex]
\frac{1997}{4} &\frac{1998}{4} &\frac{1999}{4} &\ldots
\end{array}
\right\}\subseteq \setQ\setminus\setN.
\]


\end{document}

You can actually make a new column type to ease up the entries. But I always confuse myself with >{}, <{} groups. Block selection of text seemed easier this time :)

---

EDIT: Converted to a sequence such that mathematically sensitive ones are less offended.

Here are two other ways :

Code:

\documentclass{article}
\usepackage{amsmath}

\newcommand*\mathsetfont{\mathbf}
\newcommand*\DeclareMathSet[1]{%
  \expandafter\newcommand\csname set#1\endcsname{\mathsetfont{#1}}
}
\DeclareMathSet{N}
\DeclareMathSet{Q}

\begin{document}
The equation:
\[
\left\{ \frac{y}{4} \right\} \subseteq \setQ\setminus\setN
\]
where $y \in \{ 1983, 1985, 1986, 1987, 1989, 1990, 1991, 1993, 1994, 1995, 1997, 1998, 1999 \}$
\bigskip
\hrule
\bigskip
If we let $Y = \{ 1983, 1985, 1986, 1987, 1989, 1990, 1991, 1993, 1994, 1995, 1997, 1998, 1999 \}$, then
\[
\left\{ \frac{y}{4} \,\middle|\, y \in Y\right\} \subseteq \setQ\setminus\setN
\]
\bigskip
\hrule
\bigskip
The set $Y$ could also be expressed as
\[ Y = \{ n \in \setN \mid 1983 \le n \le 1999 \} \setminus \{ 1984,1988,1992,1996\} \]
\end{document}

Another take... very scientific look:

\documentclass{article}

\usepackage{amsmath}

\newcommand{\mathsetfont}{\mathbf}
\newcommand{\DeclareMathSet}[1]{%
  \expandafter\newcommand\csname set#1\endcsname{\mathsetfont{#1}}
}
\DeclareMathSet{N}
\DeclareMathSet{Q}

\begin{document}

\[ \{n/4\mid n\in [1983, 1999]\setminus\{1984,1988,1992,1996\} \cap \setN\}\subseteq \setQ\setminus\setN \]

\end{document}

EDIT: ... or you may even completely do away with any explicit enumeration of numbers, if that's what you're after:

\[ \{n/4\mid n\in [1983, 1999] \cap \setN\ \land n \neq 4m \mid m \in \setN\}\subseteq \setQ\setminus\setN \]