```Date: Aug 22, 2013 6:23 PM
Author: namducnguyen
Subject: Re: A finite set of all naturals

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 thatodd(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 argumenthere (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
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