Minimum number of elements for a set to become group - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-23T21:19:20Z http://mathoverflow.net/feeds/question/69517 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/69517/minimum-number-of-elements-for-a-set-to-become-group Minimum number of elements for a set to become group sashank 2011-07-05T06:33:37Z 2011-07-05T06:33:37Z <p>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.</p> <p>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 ?</p>