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 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_ .

--

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There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI