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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: 2,702
Registered: 12/13/04
Re: A finite set of all naturals
Posted: Aug 23, 2013 10:12 AM
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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)

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
Read Re: A finite set of all naturals
namducnguyen
8/22/13
Read Re: A finite set of all naturals
namducnguyen
8/23/13
Read Re: A finite set of all naturals
Peter Percival
8/23/13
Read Re: A finite set of all naturals
quasi
8/23/13
Read Re: A finite set of all naturals
Peter Percival
8/23/13
Read Re: A finite set of all naturals
namducnguyen
8/23/13
Read Re: A finite set of all naturals
Peter Percival
8/24/13
Read Re: A finite set of all naturals
Peter Percival
8/24/13
Read Re: A finite set of all naturals
namducnguyen
8/23/13
Read Re: A finite set of all naturals
Shmuel (Seymour J.) Metz
8/23/13
Read Re: A finite set of all naturals
namducnguyen
8/23/13
Read Re: A finite set of all naturals
Peter Percival
8/23/13
Read Re: A finite set of all naturals
namducnguyen
8/24/13
Read Re: A finite set of all naturals
Peter Percival
8/24/13
Read Re: A finite set of all naturals
namducnguyen
8/24/13
Read Re: A finite set of all naturals
Peter Percival
8/24/13
Read Re: A finite set of all naturals
Shmuel (Seymour J.) Metz
8/25/13
Read Re: A finite set of all naturals
namducnguyen
8/25/13
Read Re: A finite set of all naturals
Peter Percival
8/25/13
Read Re: A finite set of all naturals
fom
8/25/13
Read Re: A finite set of all naturals
Shmuel (Seymour J.) Metz
8/24/13
Read Re: A finite set of all naturals
Shmuel (Seymour J.) Metz
8/24/13
Read Re: A finite set of all naturals
Shmuel (Seymour J.) Metz
8/23/13
Read Re: A finite set of all naturals
tommy1729_
8/23/13
Read Re: A finite set of all naturals
Peter Percival
8/23/13
Read Re: A finite set of all naturals
namducnguyen
8/23/13
Read Re: A finite set of all naturals
Peter Percival
8/23/13
Read Re: A finite set of all naturals
namducnguyen
8/24/13
Read Re: A finite set of all naturals
Peter Percival
8/24/13
Read Re: A finite set of all naturals
namducnguyen
8/24/13
Read Re: A finite set of all naturals
Peter Percival
8/24/13
Read Re: A finite set of all naturals
namducnguyen
8/24/13
Read Re: A finite set of all naturals
Peter Percival
8/24/13
Read Re: A finite set of all naturals
namducnguyen
8/24/13
Read Re: A finite set of all naturals
Peter Percival
8/24/13
Read Re: A finite set of all naturals
fom
8/24/13
Read Re: A finite set of all naturals
Ben Bacarisse
8/24/13
Read Re: A finite set of all naturals
namducnguyen
8/24/13
Read Re: A finite set of all naturals
fom
8/24/13
Read Re: A finite set of all naturals
Peter Percival
8/24/13
Read Re: A finite set of all naturals
fom
8/25/13
Read Re: A finite set of all naturals
Peter Percival
8/23/13
Read Re: A finite set of all naturals
Shmuel (Seymour J.) Metz

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