A group is a nonempty set G on which there is defined a binary operation (a, b) → ab satisfying the following properties. Closure: If a and b belong to G, then ab is also in G; Associativity: a(bc) = (ab)c for all a, b, c ∈ G; Identity: There is an element 1 ∈ G such that a1 = 1a = a for all a in G; Inverse: If a is in G, then there is an element a−1 in G such that aa−1 = a−1a = 1.
Does this mean , we need to have atleast three elements in a set for it to be a candidate for Group ? A set containing binary numbers ( 0 , 1 ) cannot become a group ? under any operation ?