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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 23, 2013 3:51 PM
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On 23/08/2013 1:42 PM, Peter Percival wrote:
> Nam Nguyen wrote:
>> On 23/08/2013 8:55 AM, Shmuel (Seymour J.) Metz wrote:
>>> In <ghae19tt5it7c9phdr64quip03q2dmdl29@4ax.com>, on 08/23/2013
>>> at 04:40 AM, quasi <quasi@null.set> said:
>>>

>>>> With Nam's new definition of positive/negative, I think
>>>> it's immediately provable (subject to some clarification as to what
>>>> a formula is) that odd(x) is a negative formula.

>>>
>>>> Let even(x) <-> Ey(x=2*y).
>>>
>>> Let odd(x) <-> Ey(S(x=2*y)).
>>>

>>>> Assuming Nam's definition of "formula" supports the claim that
>>>> even(x) is a positive formula, then odd(x) must be a negative
>>>> formula since odd(x) is equivalent to ~even(x).

>>>
>>> However, even(x) is equivalent to ~odd(x), so even(x) must be a
>>> negative formula.
>>>
>>> You can exclude S, but then you're no longer talking about the natural
>>> numbers.

>>
>> You seem to be confused on the issue, which is that _in the natural_
>> _numbers_ while even(x) can be positively expressed _with only_ '*'
>> can the same be said of odd(x)?
>>
>> The correct answer is "NO".
>>
>> What is _your answer_ to this question?

>
> What do you take the natural numbers to be? Are you defining them or
> are you using the usual informal definition?

What is your answer to this question of mine above?

Anything else is _irrelevant_ .

If you or Ben couldn't give me _a straightforward Yes or No answer_
on this question, let's forget about anything else.

--
-----------------------------------------------------
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

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