[FOM] Logic of irrational numbers
joeshipman@aol.com
joeshipman at aol.com
Thu Mar 5 11:57:10 EST 2009
Are you sure about this? It sounds like, if your conjecture is true,
then Schanuel's Conjecture could not be a theorem of ZFC.
-- JS
-----Original Message-----
From: Harvey Friedman <friedman at math.ohio-state.edu>
To: Foundations of Mathematics <fom at cs.nyu.edu>
Sent: Wed, 4 Mar 2009 11:22 am
Subject: [FOM] Logic of irrational numbers
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
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