Talk:Multiplication

Not just repeated addition

I am moderating the language, "multiplication is defined by repeated addition". There are serious objections to "defining" multiplication in this way from the "more basic" operation addition, first among them being that with no modification, the statement is wrong. See the articles [1] and [2] by noted mathematician and expositor Keith Devlin for more about this. The second gives references to educational authorities who agree.

You would have been right to challenge "multiplication is defined by repeated addition" if that had been what was written. The wording "Multiplication is defined in terms of repeated addition" (not mine incidentally) actually means something different and rather more subtle.

I'm not happy with introducing non-commutativity into an article at this level in this way. If you begin by defining multiplication as the "binary mathematical operation of scaling one number or quantity by another (multiplying)" and one of the "basic operations in elementary arithmetic" then it is commutative without question. Matrix multiplication etc probably belong in a paragraph at the end about generalisations. If you want to introduce such relatively sophisticated concepts into an article about elementary arithmetic, then "The most general context in which a multiplication operation exists, encompassing all of the above examples, is that of the abstract ring" is not correct (or at least a pure matter of opinion) either. The most general context is a magma, a partial binary operation with no other properties.