On Tue, Sep 11, 2012 at 10:28 AM, Joe Niederberger <niederberger@comcast.net> wrote: >>But scaling works for all of the reals easily and perfectly and exactly, no redefinition ever needed. > > Scaling as you are using it is just a synonym for real number multiplication. >
No, it's a property of binary multiplication on any subset of the real numbers.
> So give us a detailed mathematical account of the "process" (Devlin) that multiplication is that is not flat-out circular. >
Its not circular since it's not a synonym. Repeated addition and scaling are properties of the operations respectively on some or all subsets of the reals, and that these properties are not what these operations *are*. They are models of properties of some or all of the operations, not the operations themselves.
I reiterate everything I said in my last post in this thread
