On Fri, 16 Aug 2013 02:05:09 -0700, William Elliot <email@example.com> wrote:
>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)
If you don't know what "in the language of arithmetic" means it would be a good idea to refrain from answering questions about the language of arithmetic, lest you look silly.
>> 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. >>