A group in math is a set of elements that follow specific rules of operation. These rules include closure, associativity, identity, and invertibility.
To determine if x is a group, you must check if it satisfies the four group axioms: closure, associativity, identity, and invertibility. If all four axioms are met, then x is a group.
A set is closed under an operation if the result of performing that operation on any two elements in the set is also an element of the set. In other words, the operation does not produce a result that is outside of the set.
No, a group must have an identity element, which is an element that, when combined with any other element in the group, results in that same element. Without an identity element, the set cannot satisfy the group axioms.
No, a group can only have one identity element. If there are multiple identity elements, then the set cannot satisfy the group axioms because there would not be a unique identity element to combine with other elements in the set.