Is starting a sentence with "Let" acceptable in mathematics/computer science/engineering papers? I received a comment from a colleague that starting a sentence with &quot;let&quot; is not good practice. I know that starting a sentence with &quot;let&quot; is grammatically correct, so that is not the question. My question is if starting a sentence with &quot;let&quot; is good practice and acceptable in technical writing.
Here are a couple examples:


Let scalars be denoted by lower case letters.
Let x be a real number greater than zero.
Let the set of real numbers be denoted by R.
These are all acceptable. My personal preference would be to reserve &quot;let&quot; for statements that are (essentially) assignments, like the second one in the question. The other two establish notation conventions. I might say something like

We use lower case letters for scalar variables.

or

Lower case letters represent scalar variables.

and

We write R for the set of real numbers.