A Group

A group G is a collection of objects with an operation satisfying the following rules (axioms).

Today I realized that the operation is actually what defines a group, NOT the collection of objects. A collection of object is not a group (of objects) as I previously thought (probably because I was making a connection between the English meaning of the word group and the mathematical term group). Also, a group can lose it’s status if it’s operation changes but the collection of objects remains the same (if some of the axioms stop being true for the new operation).