Uncountability of the Rationals?
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From: Jesse F. Hughes on 27 Jun 2010 15:18 Tony Orlow <tony(a)lightlink.com> writes: > Your sarcasm is ill-directed. That one detects a self-contradiction in > a definition does not mean that the theory one is using is > inconsistent. It means the definition is not acceptable, which in this > case means tav is not a number, being neither finite nor infinite. I'm not sure about the above contradiction, but just today, you've said both that tav is an element of N+ and that tav is not an element of N+. That's an inconsistency. Most of us regard inconsistency as a bad thing in a theory. -- "So yeah, do the wrong math, and use the ring of algebraic integers wrong, without understanding its quirks and real mathematical properties, and you can think you proved Fermat's Last Theorem when you didn't." -- James S. Harris on hobbies
From: MoeBlee on 27 Jun 2010 16:16 On Jun 26, 6:26 pm, Tony Orlow <t...(a)lightlink.com> wrote: > At least I try to be funny.... You are so unfunny that it's not even funny. MoeBlee
From: Virgil on 27 Jun 2010 16:20 In article <a3c7fd95-3169-405e-a739-adae60178a0d(a)y11g2000yqm.googlegroups.com>, Tony Orlow <tony(a)lightlink.com> wrote: > On Jun 26, 10:36�pm, David R Tribble <da...(a)tribble.com> wrote: > > Tony Orlow wrote: > > >> Where you have a minimum positive difference between successive > > >> elements (like 1), then any infinite number of them means an infinite > > >> difference between the first and last. > > > > Jesse F. Hughes wrote: > > >> Is it your opinion that N+ has a last element? > > > > Tony Orlow wrote: > > >> No, and that's beside the point. > > > > You entirely missed the point of Jesse's question. > > > > You claim that for an infinite ordered set with a minimum difference > > between members, the set must have an infinite difference between > > the first and last elements. > > If it is truly infinite, that is, uncountable. Then {-oo, +oo}, having such an infinite difference, is uncountable? > > We've been over this a thousand times. What a shame that in that many attempts you still haven't got it right!
From: Virgil on 27 Jun 2010 16:36 In article <e950a5bb-6d8a-4c48-b321-81c9d546e901(a)u26g2000yqu.googlegroups.com>, Tony Orlow <tony(a)lightlink.com> wrote: > On Jun 26, 10:56�pm, David R Tribble <da...(a)tribble.com> wrote: > > Tony Orlow wrote: > > > There is no error. The contradiction concerning omega or tav is > > > deliberate. It doesn't exist as a number, as evidenced by its own self- > > > contradiction. > > > > Granted, you claim that omega can't exist as a natural, counting > > number, set size, or bigulosity. But how does all that keep it > > from existing as some other kind of number? > > > > Perhaps you could clarify what you mean by "number". > > A number is a location in an n-dimensional mathematical space, such > that every number is denoted by a unique n-tuple. There is no location > called omega or tav. How can you specify a number of dimensions without having a number up front? Your "definition" is thus viciously circular, and thus invalid.
From: Virgil on 27 Jun 2010 16:37
In article <6b58b1ab-5395-4889-8ae8-643aa5d1f1bb(a)z10g2000yqb.googlegroups.com>, Tony Orlow <tony(a)lightlink.com> wrote: > On Jun 26, 10:59�pm, Tim Little <t...(a)little-possums.net> wrote: > > On 2010-06-26, Tony Orlow <t...(a)lightlink.com> wrote: > > > > > There is some proof left to do, but the fact is that taking log(|x|) > > > repeatedly tends around 0, and so the probability of the root of any > > > number becoming 0 through this recursive process eventually > > > approaches 1. > > > > False. �The probability is actually zero. > > > > - Tim > > Proof, please. The one who never provides proofs is now demanding a proof? |