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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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namducnguyen

Posts: 2,674
Registered: 12/13/04
Re: A finite set of all naturals
Posted: Aug 13, 2013 2:40 AM
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On 13/08/2013 12:56 AM, quasi wrote:
> 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.


Then the answer is No: my proof wouldn't be sufficient for GC_4
or GC_6 (should they be true), but for a different reason compared
to the weak Goldbach Conjecture.

Note that in the case of G_4, (sum of 4 primes) => (sum of 2 evens);
and in the case of G_6, (sum of 6 primes) => (sum of 2 odds).

--
-----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI


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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