Uncountability of the Rationals?
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From: Virgil on 16 Jun 2010 14:58 In article <edaf41f0-7409-499d-b9af-6ab4ed06db80(a)y11g2000yqm.googlegroups.com>, Tony Orlow <tony(a)lightlink.com> wrote: > E(-2^x) ^ E(2^x) You seem to be using "^" in two incompatible senses in the same expression. If "^" is for exponentiation and "/\" is for conjunction, do you mean " E(-2^x) /\ E(2^x) " ? And, if not, what do you mean?
From: Jesse F. Hughes on 16 Jun 2010 14:57 Aatu Koskensilta <aatu.koskensilta(a)uta.fi> writes: > "Jesse F. Hughes" <jesse(a)phiwumbda.org> writes: > >> In fact, I'd be interested also in a proof that 8 is a real number. > > You can't come up with a proof on your own? Go crank your non-standard > crank, you crank. I think 8 is Julius Caesar. -- Jesse F. Hughes "If anything is true in general about Usenet, it's that people can go on and on about just about anything." -- James Harris speaks the truth.
From: Virgil on 16 Jun 2010 15:00 In article <b16ba30e-2e28-43cd-9876-a784c51c51cf(a)x21g2000yqa.googlegroups.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Imanswered this already. I do not disagree that there exists a > bijection, but within any segment of R greater than measure 2 exist > more square roots of naturals than naturals. Sure, you can find a > member in each set corresponding to a unique member of the other. They > are equicardinal. They are not equibigulous. "Equibigulous" sounds like a disease condition requiring serious surgery.
From: Virgil on 16 Jun 2010 15:03 In article <b16ba30e-2e28-43cd-9876-a784c51c51cf(a)x21g2000yqa.googlegroups.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Obviously, > natural density is wrong, since it contradict cardinality. Which > axioms must be abandoned in order to entertain natural density? Then density of physical objects must "contradict" other measures of physical properties, like volume or weight.
From: Virgil on 16 Jun 2010 15:06
In article <31594962-879f-4853-bbb7-20060b99eb08(a)z10g2000yqb.googlegroups.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Oh, I see your question. It's not a bad one, though it is outside of > the scope of IFR abd ICI, ultimately, since it is not a mapping > between N+ and another set of reals, but an expression of the relation > mapping N+ to the squares. Your point is that, according to > Bigulosity, there should be tav elements since there are tav naturals, > but there should be sqrt(tav) elements if there are sqrt(tav) squares > of naturals. That would appear to be a contradiction, granted. > However, Bigulosity does not claim to assign a size to such a set. It > is something worth considering though. If there are sets to which bigulosity does not assign sizes, ,how is it any improvement on cardinality which, given the axiom of choice, always does? |