
Re: Goldbach Conjecture
Posted:
Sep 17, 2000 8:22 AM


daniel_mcl@hotmail.com (Daniel McLaury) wrote: > An example of the "law of small numbers" in real maths > is given by the conjecture that Li(x) is always less than Pi(x). > This is true for values well over a googol, but eventually it > becomes false for all values over a certain number.
Slight correction: Littlewood actually showed that Li(x)  Pi(x) alternates in sign infinitely often, and gave an upper bound for the position of the first sign change.
Another example is Borsuk's conjecture on decomposing a bounded set in d dimensions into d+1 sets of strictly smaller diameter. It was shown to be false in dimension 1325 (and it's now known to be false in at least dimensions 561 and up).
 Erick

