To better understand what I'm asking about, let's immediately define some examples. Imagine that you are writing some paper which involves a lot of math narrative. And you have a term, say, *computing unit* (processor). Then at some point you introduce a mathematical variable, which you would use in formulas and text, $m$ and you define it as *number of computing units* (verbal definition).

**Question #1:** When I want to refer to $m$ in the text, I can do it in 3 ways:

- One could observe linear speedup given increasing number of computing units $m$ in the system.
- One could observe linear speedup given increasing number of computing units in the system.
- One could observe linear speedup given increasing $m$ in the system.

Is there any general stylistic guideline on which one to prefer, when, and why? If not, then I'd still like to hear your personal opinion as long as it is backed up by healthy reasoning and/or authority.

I personally prefer #1 because as soon as $m$ is defined, I believe that it is easier for reader to follow and constantly stay in context of narrative if I refer to this quantity with verbal definition (which reminds reader of its purpose) and with variable (which assures reader that indeed I refer to these computing units and not other ones and that formulas involving $m$ presented before or after are indeed connected with current sentence/statement). Can you think of any case where this method #1 would be harmful/irritating/misleading?

**Question #2:** While the first question was about general guideline, this one is about positioning of verbal definition with respect to variable. So let's assume that we praise method #1 from previous question, then there are 2 ways to write it:

- One could observe linear speedup given increasing number of computing units $m$ in the system.
- One could observe linear speedup given increasing number $m$ of computing units in the system.

Any general guideline? Pros and cons? You personal opinion?

Maybe that example was not so good at demonstrating possible confusion, but here is another one:

- Consider average velocity of stream $v$.
- Consider average velocity $v$ of stream.
- Consider average stream velocity $v$.

Notice how #1 confuses about whether $v$ refers to "stream" or "average velocity of stream". #2 and #3 read better. Would you even omit word "stream" in narrative if you've already defined $v$ as "average velocity of stream" once?

**Question #3:** Punctuation. The general guideline which is well-known among technical writers, I suppose, is: *a text (narrative) involving math is still a text in the first place and has to obey the same punctuation rules as any other text not related to math*. Well, then consider the following sentence:

Our valuable employee, Alexander, was granted permission to access this room.

Notice how "Alexander" is surrounded with commas. Following this rule, shouldn't we apply it to math narrative then? For example:

Average stream velocity, $v$, is a very important quantity in this context.

Can you feel the analogy between two? What are your thoughts about it?