Re: Svara that Goldbach's Conjecture is Unprovable

From: xx (yy_at_zz.zz)
Date: 07/12/04 

Date: Mon, 12 Jul 2004 14:16:48 -0400

Michael N. Christoff wrote:
> "Craig Feinstein" <cafeinst@msn.com> wrote in message
> news:b671fc3e.0407120601.7f74f7c6@posting.google.com...
>
>> The argument is as follows. Its very similar to a previous post
>> that I made which argues that Twin Primes is unprovable. I'll let
>> you judge whether this is a rigorous proof or not. I'm not claiming
>> that it is or that it is not - It's just for fun:
>>
>> Let set S be the set of all q such that 0<q<2n and q is prime. Let
>> set T be the set of all q such that 0<q<2n and 2n-q is prime.
>>
>> Then Goldbach's Conjecture is equivalent to the intersection of
>> sets S and T being nonempty for each natural number n.
>>
>> Now, the condition which defines set S, that q is prime, does not
>> give any information about the factors of 2n-q, so it does not give
>> any information about whether or not 2n-q is prime.
>>
>> And the condition which defines set T, that 2n-q is prime, does not
>> give any information about the factors of q, so it does not give
>> any information about whether or not q is prime.
>>
>> Therefore, the two conditions which define the two sets are
>> independent from one another, meaning that the only way to
>> determine whether the intersection of the two sets, S and T, is
>> nonempty is to directly calculate the elements in the intersection
>> of S and T, i.e., test if there is a q such that q and 2n-q are
>> both prime. But this would take an infinite amount of time, since
>> one would have to test this for each natural number n. Therefore,
>> Goldbach's Conjecture is unprovable. QED
>>
>> For those of you who don't buy the argument, let me explain this in
>> another way: One can define set S as the days in the year 2003 in
>> which twins were born in hospital A. And define set T as the days
>> in the year 2003 in which twins were born in hospital B. (A and B
>> are two different hospitals in different parts of the world.) The
>> conditions which define sets S and T have nothing to do with one
>> another, i.e., they are independent from one another. Therefore,
>> the only way to determine whether the intersection of sets S and T
>> is nonempty is to directly calculate the elements in the
>> intersection of sets S and T. This is obviously feasible to do
>> since the number of days in the year 2003 is finite, but if one had
>> to do it for each year until the end of time and prove that there
>> is always a day in each year when both hospitals give birth to
>> twins, one would have to wait an eternity to do such.
>>
>> Anyway, I welcome comments.
>>
>
>
> Hi Craig. This sounds similar to your proof idea for p!=np. In that
> proof, if I recall correctly, you claimed (without adequate proof)
> that a single solution to the problem existed (in that case the
> problem was subset-sum), and then claimed that this single solution
> required at least a super-polynomial amount of computation to solve
> (hence subset-sum must be in NP-P so P != NP). In this proposition
> you state:
>
> "the only way to determine whether the intersection of the two sets,
> S and T, is nonempty is to directly calculate the elements in the
> intersection of S and T"
>
> You still need to prove that this truly is 'the only way'.
>
>
>
> l8r, Mike N. Christoff
>
>

Good day Craig.

As well, similar to your argument that the 3n+1 conjecture is
unprovable, in the paper you posted to arXiv:math.GM.

Also, to the argument that Riemann's conjecture is unprovable, in
another paper you posted in the same place (later withdrawn).

I see a general principle emerging here, not necessarily a theorem,
but perhaps a svara-theorem.

xx

Relevant Pages

  • Re: Svara that Goldbachs Conjecture is Unprovable
    ... > Then Goldbach's Conjecture is equivalent to the intersection of sets S ... > and T being nonempty for each natural number n. ... > hospitals give birth to twins, one would have to wait an eternity to ...
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  • Svara that Goldbachs Conjecture is Unprovable
    ... Then Goldbach's Conjecture is equivalent to the intersection of sets S ... and T being nonempty for each natural number n. ... the year 2003 in which twins were born in hospital B. (A and B are two ... hospitals give birth to twins, one would have to wait an eternity to ...
    (sci.math)
  • Re: Svara that Goldbachs Conjecture is Unprovable
    ... > Then Goldbach's Conjecture is equivalent to the intersection of sets S ... > and T being nonempty for each natural number n. ... But it is perfectly possible that the intersection be empty. ...
    (sci.math)
  • Re: Svara that Goldbachs Conjecture is Unprovable
    ... >> made which argues that Twin Primes is unprovable. ... >> whether the intersection of the two sets, S and T, is nonempty is to ... Therefore, Goldbach's Conjecture ... to prove or disprove Goldbach's conjecture would take an infinite amount ...
    (sci.math)
  • Independent sets problem
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