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.
“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?”