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

 Messages: [ Previous | Next ]
 namducnguyen Posts: 2,777 Registered: 12/13/04
Re: A finite set of all naturals
Posted: Aug 24, 2013 1:43 AM

On 23/08/2013 11:35 PM, Peter Percival wrote:
> Nam Nguyen wrote:
>> On 23/08/2013 7:51 AM, Peter Percival wrote:
>>> quasi wrote:
>>>> Peter Percival wrote:
>>>>> Nam Nguyen wrote:
>>>>>>
>>>>>> I certainly meant "odd(x) can _NOT_ be defined as a
>>>>>> positive formula ...".

>>>>>
>>>>> Prove it.

>>>>
>>>> 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).
>>>>
>>>> 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).
>>>>
>>>> So, conceding that, where does he go with it?
>>>>
>>>> quasi

>>>
>>> But who's to say that there isn't a positive formula phi with one free
>>> variable x such that phi(x) <-> odd(x)?

>>
>>

>>> phi may be taken as a definition of odd.
>>
>> Sure. If in the language of arithmetic - or L(*), you defined:
>>
>> odd(x) <-> Ey(x=2*y)

>
> What is 2 in L(*)? Elsewhere you say 2 is SS0.

Actually I had defined 2 in L(0,<,*) not just L(*). (Same difference
in this context).

>
>> then _this_ odd(x) would be positive as expressed in _both_ languages.
>>
>> That still doesn't "invalidate" the _definitions_ .

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