This may be obvious to some people, but not to some students who signed up for a math lecture in English, in a country that doesn’t speak English.

**The set** of positive integers is the set of **all** positive integers. **A set** of positive integers is a subset of the set of positive integers.

Example sentences:

“A partition of a set S is **a set** of nonempty subsets of S such that every element x in S is in exactly one of these subsets.”

“**The set** of all men is a proper subset of **the set** of all people”

“How can I prove that **a set** of natural numbers always have a minimum?”

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