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Topic: A finite set of all naturals
Replies: 32   Last Post: Aug 15, 2013 4:07 PM

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 quasi Posts: 12,067 Registered: 7/15/05
Re: A finite set of all naturals
Posted: Aug 13, 2013 2:01 AM

Nam Nguyen wrote:
>quasi wrote:
>> Nam Nguyen wrote:
>>>
>>> More than once, I was asked what the difference between the
>>> Goldbach Conjecture and its weaker form that an odd number
>>> greater than 7 is the sum of three odd primes.
>>>
>>> The point is though the essences of the 2 conjectures are
>>> drastically different: _an odd number can not be defined
>>> without addition_ while an even number can (as per Def-03b
>>> above).

>>
>> Consider the following statements:
>>
>> GC_2: All sufficiently large even numbers can be expressed as
>> the sum of 2 primes.
>>
>> GC_4: All sufficiently large even numbers can be expressed as
>> the sum of 4 primes.
>>
>> GC_6: All sufficiently large even numbers can be expressed as
>> the sum of 6 primes.
>>
>> etc ...
>>
>> It seems you claim to have proved:
>>
>> "It impossible to know whether or not GC_2 is true."

>
>That's not what I claimed ...
>
>... my much more restricted claim to prove (as opposed to my
>
>(*) If the Goldbach conjecture is true in the natural numbers,
> then it's impossible to structure theoretically prove, verify
> it so.

OK.

>> Would your proof method also suffice to prove the same for
>> GC_4? For GC_6? etc?

>
>Before this, do you agree there has been a misunderstanding
>on what I had said to Virgil I could prove here, in relation
>to GC_2?

Sure, no problem -- agreed.

>_still_ stand?

Yes.

quasi

Date Subject Author
8/12/13 Ben Bacarisse
8/12/13 Peter Percival
8/12/13 fom
8/12/13 Ben Bacarisse
8/12/13 namducnguyen
8/12/13 namducnguyen
8/12/13 antani
8/12/13 namducnguyen
8/13/13 Marshall
8/13/13 quasi
8/13/13 namducnguyen
8/13/13 quasi
8/13/13 namducnguyen
8/13/13 namducnguyen
8/13/13 quasi
8/13/13 namducnguyen
8/14/13 quasi
8/14/13 namducnguyen
8/14/13 quasi
8/14/13 namducnguyen
8/15/13 namducnguyen
8/15/13 Virgil
8/15/13 namducnguyen
8/15/13 antani
8/13/13 antani
8/13/13 Peter Percival
8/13/13 Ben Bacarisse
8/13/13 namducnguyen
8/14/13 Peter Percival
8/14/13 Shmuel (Seymour J.) Metz