Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: Formally Unknowability, or absolute Undecidability, of certain arithmeticformulas.
Posted:
Jan 27, 2013 2:26 PM


On 27/01/2013 12:07 PM, Frederick Williams wrote: > Nam Nguyen wrote: >> >> In some past threads we've talked about the formula cGC >> which would stand for: >> >> "There are infinitely many counter examples of the Goldbach Conjecture". >> >> Whether or not one can really prove it, the formula has been at least >> intuitively associated with a mathematical unknowability: it's >> impossible to know its truth value (and that of its negation ~cGC) in >> the natural numbers. > > No one thinks that but you.
If I were you I wouldn't say that. Rupert for instance might not dismiss the idea out right, iirc.
> Its truth value might be discovered tomorrow.
You misunderstand the issue there: unknowability and impossibility to know does _NOT_ at all mean "might be discovered tomorrow".
It's impossible to know of a solution of n*n = 2 in the naturals means it's impossible to know of a solution of n*n = 2 in the naturals. Period.
It doesn't mean a solution of n*n = 2 in the naturals "might be discovered tomorrow", as you seem to have believed for a long time, in your way of understanding what unknowability or impossibility to know would _technically mean_ .
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI 



