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Topic: A finite set of all naturals
Replies: 43   Last Post: Aug 25, 2013 4:38 PM

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 namducnguyen Posts: 2,777 Registered: 12/13/04
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:
>> 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

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

Date Subject Author
8/22/13 namducnguyen
8/22/13 namducnguyen
8/23/13 Peter Percival
8/23/13 quasi
8/23/13 Peter Percival
8/23/13 namducnguyen
8/23/13 Peter Percival
8/24/13 Peter Percival
8/24/13 namducnguyen
8/23/13 Shmuel (Seymour J.) Metz
8/23/13 namducnguyen
8/23/13 Peter Percival
8/23/13 namducnguyen
8/24/13 Peter Percival
8/24/13 namducnguyen
8/24/13 Peter Percival
8/24/13 Shmuel (Seymour J.) Metz
8/25/13 namducnguyen
8/25/13 Peter Percival
8/25/13 fom
8/25/13 Shmuel (Seymour J.) Metz
8/24/13 Shmuel (Seymour J.) Metz
8/24/13 Shmuel (Seymour J.) Metz
8/23/13 tommy1729_
8/23/13 Peter Percival
8/23/13 namducnguyen
8/23/13 Peter Percival
8/23/13 namducnguyen
8/24/13 Peter Percival
8/24/13 namducnguyen
8/24/13 Peter Percival
8/24/13 namducnguyen
8/24/13 Peter Percival
8/24/13 namducnguyen
8/24/13 Peter Percival
8/24/13 fom
8/24/13 Ben Bacarisse
8/24/13 namducnguyen
8/24/13 fom
8/24/13 Peter Percival
8/24/13 fom
8/25/13 Peter Percival
8/23/13 Shmuel (Seymour J.) Metz