# Definite article in Maths: "(the) function f"

Is the definite article correct/necessary in sentences like the following?

``````A line that intersects (the) circle C.
We can see that (the) function f has a maximum at x=0.
Draw a line past (the) edge E.
``````

I am aware that definite articles must not be used in things like "in Figure 3" or "see Equation 7", because here "Figure" and "Equation" are treated as proper nouns (and thus capitalized). But in other kind of sentences as the previous ones, I am unsure about whether it is also correct to omit the definite article or not.

• Yes, an article is required in your second example (the zero article in ungrammatical there). The most common and idiomatic choice is the definite article; one conceptual justification for that choice, if you want it, is there is only one function with the definition `f`. Any other function defined as `f` is defined would be the same function as `f`. A rose by any other name would smell as sweet, and so forth. Now, it's possible to use the indefinite article instead, but it's less common to do so. May 3, 2015 at 11:50
• The last example, with `edge E`, is a case where you could use the zero article, because `E`, there, is acting like a proper noun (a named thing, qualified "edge"). The definite article is also fine. May 3, 2015 at 11:53
• It's more common to say "the function f", but it's possible to just say "function f" with no article. See Ngram. I don't perceive any difference between "edge E" (with no article) and "function f" (with no article). In both cases, E and f are acting like proper nouns (like President Roosevelt). I'd suggest using "the function f", but be consistent. May 3, 2015 at 11:53
• The above is mathtextbookspeak. In mathtextbookspeak the use of "the" is optional (and usually omitted) in all the cases you list. Nothing wrong as shown. (Consider that "circle C", eg, is essentially a proper noun.) May 3, 2015 at 12:08
• I agree with @PeterShor and not with Dan Bron: the is optional in the second sentence.
– Drew
May 4, 2015 at 2:11