The discussion focuses on determining the number of distinct commutative binary operations that can be defined on sets of 2 and 3 elements. For a set of 2 elements, such as {a, b}, the operations a*a, a*b, b*a, and b*b must be defined, leading to a finite number of combinations. The same logic applies to a set of 3 elements, where the operations must also be defined for all pairs. The conclusion is that the number of possible operations is not infinite, as initially assumed by one participant.
PREREQUISITESMathematics students, educators, and anyone interested in algebraic structures and set theory will benefit from this discussion.
Dick said:If '*' is the operation and {a,b} is the set of two elements, then to define the operation you need to define a*a, a*b, b*a and b*b in the set {a,b}. That's hardly an infinite number of possibilities.