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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: 10,232
Registered: 7/15/05
Re: A finite set of all naturals
Posted: Aug 13, 2013 2:01 AM
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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
>own about cGC) would be:
>
>(*) 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.

>If you do agree, would your questions about GC_4 and GC_6
>_still_ stand?


Yes.

quasi


Date Subject Author
8/12/13
Read Re: A finite set of all naturals
Ben Bacarisse
8/12/13
Read Re: A finite set of all naturals
Peter Percival
8/12/13
Read Re: A finite set of all naturals
fom
8/12/13
Read Re: A finite set of all naturals
Ben Bacarisse
8/12/13
Read Re: A finite set of all naturals
namducnguyen
8/12/13
Read Re: A finite set of all naturals
namducnguyen
8/12/13
Read Re: A finite set of all naturals
antani
8/12/13
Read Re: A finite set of all naturals
namducnguyen
8/13/13
Read Re: A finite set of all naturals
Marshall
8/13/13
Read Re: A finite set of all naturals
quasi
8/13/13
Read Re: A finite set of all naturals
namducnguyen
8/13/13
Read Re: A finite set of all naturals
quasi
8/13/13
Read Re: A finite set of all naturals
namducnguyen
8/13/13
Read Re: A finite set of all naturals
namducnguyen
8/13/13
Read Re: A finite set of all naturals
quasi
8/13/13
Read Re: A finite set of all naturals
namducnguyen
8/14/13
Read Re: A finite set of all naturals
quasi
8/14/13
Read Re: A finite set of all naturals
namducnguyen
8/14/13
Read Re: A finite set of all naturals
quasi
8/14/13
Read Re: A finite set of all naturals
namducnguyen
8/15/13
Read Re: A finite set of all naturals
namducnguyen
8/15/13
Read Re: A finite set of all naturals
Virgil
8/15/13
Read Re: A finite set of all naturals
namducnguyen
8/15/13
Read Re: A finite set of all naturals
antani
8/13/13
Read Re: A finite set of all naturals
antani
8/13/13
Read Re: A finite set of all naturals
Peter Percival
8/13/13
Read Re: A finite set of all naturals
Ben Bacarisse
8/13/13
Read Re: A finite set of all naturals
namducnguyen
8/14/13
Read Re: A finite set of all naturals
Peter Percival
8/14/13
Read Re: A finite set of all naturals
Shmuel (Seymour J.) Metz

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