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"an example to show" is correct and usable in written English.
You can use it when you want to introduce an example that provides proof or further explanation. For example, "The following example will show why this approach is effective."
Exact(60)
Parabolas are used as an example to show how to move sprites along mathematical functions.
Diffusively coupled map lattice is used as an example to show the suitability of the method.
Finally, we provide an example to show the effectiveness of the theoretical results.
Besides, this paper also presents an example to show how this type of inlet is designed.
Also, the Jiangyin Bridge was taken as an example to show the application of the buffeting-based selection method.
In what follows, we give an example to show this.
We next give an example to show this.
Next, we give an example to show this phenomenon.
Here's an example to show how the semantics works in a technical way.
In this section, we shall construct an example to show the applications of Theorem 3.1.
Finally, we will give an example to show the advantages of our results.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com