The question above seems to ask: "Is the Goldbach conjecture independent of ___" for some formal system (Peano, ZFC, etc.). The formalized version linked to, though, has a clear answer: true. That's because Ap1p2[prime(p1) /\ prime(p2) /\ (p1+p2 < x \/ x < p1+p2)] is false, and so aGC(x) simplifies to odd(x) \/ (x < SSS0). Consequently, cGC is equivalent to "there are infinitely many nonnegative integers that are either odd or less than 3" which is of course true. But even if the right side of aGC was fixed cGC would still be trivially true for the same reason.
login/create account
Drupal
CSI of Charles University
Formalization
The question above seems to ask: "Is the Goldbach conjecture independent of ___" for some formal system (Peano, ZFC, etc.). The formalized version linked to, though, has a clear answer: true. That's because Ap1p2[prime(p1) /\ prime(p2) /\ (p1+p2 < x \/ x < p1+p2)] is false, and so aGC(x) simplifies to odd(x) \/ (x < SSS0). Consequently, cGC is equivalent to "there are infinitely many nonnegative integers that are either odd or less than 3" which is of course true. But even if the right side of aGC was fixed cGC would still be trivially true for the same reason.