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 <> 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.