> On Fri, 16 Aug 2013, Peter Percival wrote: > > > Can addition be defined in terms of multiplication? > I.e., is there a formula > > in the language of arithmetic > > > > x + y = z <-> ... > > > > such that in '...' any of the symbols of arithmetic > except + may occur? Or, > > alternatively, is there a formula in the language > of arithmetic > > > > x + y = ... > > > > with the same requirement? > > x + y = log(e^x * e^y)
the logaritm has branches on the complex plane Im afraid.
On the other hand, I dont call it " silly " as Ullrich likes to do.
> > > The symbols of arithmetic (for the purpose of this > question) are either > > > > individual variables, (classical) logical > constants including =, > > S, +, *, and punctuation marks; > > > > or the above with < as an additional binary > predicate symbol. > >