
Re: A finite set of all naturals
Posted:
Aug 22, 2013 6:23 PM


On 22/08/2013 2:51 PM, Shmuel (Seymour J.) Metz wrote: > In <JaiRt.143228$po1.110557@fx15.iad>, on 08/22/2013 > at 12:26 AM, Nam Nguyen <namducnguyen@shaw.ca> said: > >> But isn't it true that GC, primes, even(), odd(), are ultimately >> related > > Whatever their relationship, that doesn't address the ability to > define even() and odd() nonrecursively.
Whatever you may wish to say, that doesn't negate the fact that odd(x) can be defined as a positive formula with only the symbol '*' alone, as we could with even(x) which is the center of the argument here (in this thread).
> >> in the context of the "natural numbers", > > In that context, S() is available. > >> Right, but we've been discussing if we could express odd(x) with >> only * and without S > > Then it's time to stop referring to the naturals, either in the > subject or in the body.
No it's _not_ : it's true that even(x) can be defined _with or without_ '*', while odd(x) is _not_ : _still in reference to the natural numbers_ .
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI

