On Sat, Sep 15, 2012 at 1:37 PM, Joe Niederberger <firstname.lastname@example.org> wrote: > Paul Tanner III Says: >>>Repeated addition is merely a derivable property of the two operations of such a field like the real numbers, derived in such a field from just some of the algebraic properties > > Joe N said: >>Says you. I say it refers to a family of related procedures for computing addition and as such is a proud and rather ancient member of the incredibly important part of mathematics known today as computational mathematics. > > In addition, it can also refer to various *definitions* of addition; to take an example, as in Peano Arithmetic. >
Only in the natural numbers and with some work, the integers. In the rational numbers a new definitions for multiplication has to be given in terms of the newly defined numbers called rational numbers, defined as equivalence classes of ordered pairs of integers.