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