# Specific case of using articles in mathematics

My czech book on English in mathematics has a section about choosing the right article. It says:

Use the indefinite article when you are referring to each element of a class. For example: Mersenne primes are related to perfect numbers.

And then:

Use the definite article when you are referring to all elements of a class. For example: The harmonics numbers are the numbers H^n for \alpha > 1 defined by the formula...

I am deeply confused since I do not get the difference between the examples. I do not get the difference between each element and all elements neither.

• That's really unhelpful. "Use indefinite article" [sic] with a plural example. And both those sentences should start with "Use the ... article when..." Feb 8, 2017 at 23:55
• Edited. Why do you think it is unhelpful?
– peter
Feb 8, 2017 at 23:56
• It's unhelpful because the indefinite article (a/an) cannot be used with plurals. Have a look at our standard go-to post: Simple rules for articles. Feb 8, 2017 at 23:58
• Are those sentences actually quotations in English from your book? Or are they written in Czech and you have translated them into English for this question? Feb 8, 2017 at 23:59
• The article you need to be careful about in maths is "the."Consider:
– Airymouse
Feb 9, 2017 at 1:26

It looks rather confusing indeed: the chosen examples do little to illustrate the concept as they seem to refer both to all elements of a class, and the first one doesn't contain any article worth mentioning. Hopefully the following examples may help clarify the point a little better.

Indefinite article: "An element of the harmonic series has the form 1/n". Of course this refers actually to all elements of the harmonic series, but formally only a generic one is considered. 'An' might be easily replaced by 'each' without altering the sense of the sentence.

Definite article: "By convention the first prime number is 2, although 1 fits the definition as well". Here we are talking about a specific element of a set, the first one.

Definite article: "The elements of an abelian group obey the axiom of commutativity". Here we are explicitly considering all elements of the group collectively rather than a single, generic one.

• How would you argue the following example: Mersenne primes are related to perfect numbres. It seems to me like it should go with the definite article, but my book says it shouldnt.
– peter
Feb 9, 2017 at 11:34
• That's a tricky point. I'm afraid I cannot provide a decent explanation, but hopefully someone else will. It is not because of the proper name (I would say "prime numbers are...", not "the prime numbers are..."), yet saying "elements of the Klein group are..." without a the would feel very wrong.
– user49115
Feb 9, 2017 at 16:35