1

I am using the following to align the two equations. However, they are not vertically on the same level. How should I fix it?

\documentclass{article}

\usepackage{amsmath}

\begin{document}  
\begin{equation*}
\begin{split}
G(Q,N)=\sum\limits_{Q_i \in N} F(Q_i,N); \;\;
\end{split}
\begin{split}
F(n,N)= 
\begin{cases}
1, & \text{if } n > N \\
0.5, & \text{if } n = N \\
0, & \text{otherwise}
\end{cases}
\end{split}
\end{equation*}
\end{document} 

enter image description here

6

Don't set each part in a split. Instead, just separate them with a \qquad (or some other horizontal space). This ensures that the math axis is not adjusted.

enter image description here

\documentclass{article}

\usepackage{amsmath}

\begin{document}

\[
  G(Q,N) = \sum\limits_{Q_i \in N} F(Q_i,N); \qquad
  F(n,N) = \begin{cases}
    1,   & \text{if } n > N \\
    0.5, & \text{if } n = N \\
    0,   & \text{otherwise}
  \end{cases}
\]

\end{document}

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