quasi
Posts:
12,067
Registered:
7/15/05


Re: A finite set of all naturals
Posted:
Aug 13, 2013 3:56 AM


Nam Nguyen wrote: >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 Def03b >>>>> 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.
What reason?
>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).
Is the above sentence supposed to be the reason why your proof method can't generalize from G_2 to G_4 or G_6?
quasi

