# Avoid “Respectively”

In many cases, using the word “respectively” makes sentences hard to parse because it requires the reader to map each item in a list based on its position. For example, “Let $x$ and $y$ be the width and height of a rectangle, respectively,” can be more clearly stated, “Let $x$ be the width and $y$ be the height of a rectangle.” By placing the definition of symbol next to the symbol, you allow readers to glean the meaning of each withing needing to backtrack or remember the order that $x$ and $y$ were written.

Another example comes from an actual paper:

Consider a nonlinear system

$$\begin{aligned}

\dot{x} & =f(x) \\

y & =h(x)

\end{aligned}$$where \(f\) and \(h\) are locally Lipschitz continuous and continuous, respectively.

This can be improved (and shortened) by removing “respectively”.

Consider a nonlinear system

$$\begin{aligned}

\dot{x} & =f(x) \\

y & =h(x)

\end{aligned}$$where \(f\) is locally Lipschitz continuous and \(h\) is continuous.

Sometimes rewritten a sentence to remove “respectively” may lengthen it significantly or may introduce tiresome repetition. In such cases, use your judgement to decide whether the improved clarity is worth the increased verbosity.