
Re: A finite set of all naturals
Posted:
Aug 22, 2013 6:24 PM


On 22/08/2013 4:23 PM, Nam Nguyen wrote: > 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).
I certainly meant "odd(x) can _NOT_ be defined as a positive formula ...".
> >> >>> 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

