Kirby says: >In that respect, addition and multiplication are similar, with their distinction so far coming down to choice of operator (commonly + and *) and choice of representation for an identity element (commonly 0 vs 1).
>Defining multiplication in terms of addition is not a bad ingredient to throw in, but likewise thrown in should be sets wherein multiplication is defined, but not addition.
Similar? A bit - the identity element is certainly similar. Related? Of course.
But if someone can show why families of 3 related binary operations do not arise similar interest and passion, then one can truly say he/she has understood.