The problem asks whether "A collection of students who sing well" is a set, based on the definition of a set. Specifically, it is mentioned that the criterion for defining a set is subjective and not well-defined.
2025/5/7
1. Problem Description
The problem asks whether "A collection of students who sing well" is a set, based on the definition of a set. Specifically, it is mentioned that the criterion for defining a set is subjective and not well-defined.
2. Solution Steps
A set is a well-defined collection of distinct objects, considered as an object in its own right. The key property of a set is that it is well-defined, meaning that there is a clear criterion for determining whether an object belongs to the set or not.
In this case, the collection is of "students who sing well". The term "sing well" is subjective. There is no objective, universally agreed-upon standard for determining whether someone sings well. Different people may have different opinions on who sings well. Therefore, the criterion for belonging to this collection is not well-defined.
3. Final Answer
A collection of students who sing well is not a set because the criterion "sing well" is subjective and not well-defined.