[FOM] Logic of irrational numbers
Harvey Friedman
friedman at math.ohio-state.edu
Wed Mar 4 11:22:40 EST 2009
Here are two wild conjectures that people might find interesting.
For positive integers n and positive real numbers x, let x^[n] =
x^...^x, where there are n >= 1 x's.
WILD CONJECTURE 1. There exists n >= 1 such that "e^[n] is irrational"
can be proved using large cardinals, but not in ZFC.
WILD CONJECTURE 2. Various basic facts about {n: e^[n] is irrational}
can be proved using large cardinals, but not in ZFC.
I am not going to try to prove or refute these wild conjecture!
Harvey Friedman
More information about the FOM
mailing list