Articles modifying nouns assigned mathematical symbol

Question

In documents including mathematics, people often specify a quantity by putting the name and mathematical symbol of it, as follows:

• Suppose that quantity A is positive;
• Let variable X be deterministic;
• Multivariable function f takes two variables;
• Let us consider directed graph G;
• Entropy S always increases.

I would like to ask about articles before those expression, say "the variable X".

I thought that the rule of articles (a/the) was still the same as usual even in this case. The is used to refer to specific or particular nouns; a/an is used to modify non-specific or non-particular nouns.

By following these rules, the above-stated expressions should be fixed by putting articles. if the above-stated quantities are specified, you could say "the quantity A", "the directed graph G" and "the entropy S", etc. Conversely, if not specified, those are written as "a quantity A", "a directed graph G" and "an entropy S", etc.

However, a friend of mine who is a native English speaker taught me such articles should be eliminated such as

• "Quantity A represents a vertex of directed graph G".

I felt that

• "A quantity A represents a vertex of the directed graph G"

would be better.

Must I remove articles modifying such expressions such as "quantity A" and "entropy S"?

Answer 1

Names (including names of variables) often follow special grammatical patterns, and these may be genre-dependent. An analogy can be made to "acclaimed actor Brad Pitt", which does not require an article in news writing:

• We spoke yesterday with acclaimed actor Brad Pitt.

It is not wrong to say "the acclaimed actor Brad Pitt", but the definite article isn't really necessary (in the news genre at least).

General rules about grammar are not absolute, so it is best to model your writing on the norms you see in the genre.