Uncountability of the Rationals?
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From: Tony Orlow on 27 Jun 2010 10:25 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.
From: Tony Orlow on 27 Jun 2010 10:25 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. Tony
From: Tony Orlow on 27 Jun 2010 10:36 On Jun 26, 11:12 pm, David R Tribble <da...(a)tribble.com> wrote: > Tony Orlow wrote: > > N+ is the standard countably infinite set of Bigulosity "tav". All > > other countably infinite sets are measured therewith. > > Well, then how about showing us how to measure the bigulosity > of a set larger[*] than N+: > G = { 1, {1}, > 2, {1,2}, {2,3}, > 3, {1,2,3}, {2,3,4}, {4,5,6}, > 4, {1,2,3,4}, {2,3,4,5}, {3,4,5,6}, {4,5,6,7}, > ... } > > You can see how G is built up from members of N+, where > the members are displayed in rows above for clarity. Each > row starts with the next natural k from N+, followed by k more > elements, each one being a set of k elements itself. Thus > each row contains k+1 elements. > > So it would appear that the size[*] of G is something like: > (1+1) + (2+1) + (3+1) + (4+1) + ... > = 2 + 3 + 4 + 5 + ... > It's obvious that G is a countable[*] set. > > So what would the bijection between N+ and G be, in order > to compute the bigulosity[*] of G? > > [*] Terms in Tony's BO Theory.
From: Jesse F. Hughes on 27 Jun 2010 10:46 Tony Orlow <tony(a)lightlink.com> writes: > On Jun 26, 10:32 pm, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: >> Tony Orlow <t...(a)lightlink.com> writes: >> >> > Rather, >> >> > |N+|=tav >> >> > Thus taveN+ >> >> > tav=|N+| and |N+|=tav. >> >> > True. >> >> >> That's not what I proved and you didn't point out any mistake. >> >> >> Nonetheless, I'm fascinated to learn that tav is in N+. N+ contains >> >> nothing but finite numbers, as you've said previously. Thus, tav is >> >> a finite number. >> >> >> Agreed? >> >> > Absolutely not!!! >> >> > As already proven, tav is neither finite nor infinite, and therefore >> > exists only virtually, or "potentially". If we assign this size "tav" >> > to that set, then it is not defined as belonging to either group of >> > quantities. >> >> I don't understand any of those words. Let's try again. Do you agree >> with each of the following? >> >> (1) Every element of N+ is a finite natural number. > > Yes. > >> >> (2) Tav is an element of N+. > > No, tav is not a number, and therefore cannot be a member of this set > of numbers. > > Tav is a variable Bigulosity, not any kind of actual count that would > qualify as even an extended natural. Oh. So, when you wrote: >> >> > Rather, >> >> > |N+|=tav >> >> > Thus taveN+ ^^^^^^^^^^^ NOTE THIS! >> >> > tav=|N+| and |N+|=tav. >> >> > True. you didn't mean tav e N+. -- Jesse F. Hughes "A gorgeous display of homoerotic lust." -- Review blurb found on the back of a Chinese black market "Dawn of the Dead" DVD
From: Brian Chandler on 27 Jun 2010 14:15
cbrown(a)cbrownsystems.com wrote: > On Jun 26, 6:47 pm, Tony Orlow <t...(a)lightlink.com> wrote: > > On Jun 26, 8:53 pm, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > > > > Nonetheless, I'm fascinated to learn that tav is in N+. N+ contains > > > nothing but finite numbers, as you've said previously. Thus, tav is > > > a finite number. > > > > > Agreed? > > > > Absolutely not!!! > > > > As already proven, tav is neither finite nor infinite, and therefore > > exists only virtually, or "potentially". > > So when you talk about tav, it's from the same point of view as when I > talk about samekh. Well, steady on. I claim some ownership over tav -- I was, after all, only following our DL, and "declaring a unit infinity". I meant, of course, to give the full version, and declare that tav is an existent, fully-non-contradictory unit infinity, infinite unity, the full Monty. Unfortunately a finger slipped (slipped again on my last post, leaving some odd bits near the end, but no-one has noticed yet), and I only said I thought 'tav' was a better name than omega. What have I done? Created a monster? Now DL starts telling me "tav is not finite", "tav is not infinite" (since DL says "infinite" means more than "finite", and "finite" means less than "infinite", I suppose that leaves tav more or less in the middle). Here are a few more recent pronouncements from our DL: > N+ is the standard countably infinite set of Bigulosity "tav". All > other countably infinite sets are measured therewith. So tav _is_ the bigulosity of N+... > Well, tav and zillion are required as primitive units in addition to > 1. They must be declared. OK, I do declare... > As already proven, tav is neither finite nor infinite, and therefore > exists only virtually, or "potentially". If we assign this size "tav" > to that set, then it is not defined as belonging to either group of > quantities. Virtually, schmirtually... > Only if you consider w, or 'tav', or whatever, to be some actual > infinite number, um, after all the other ones ended, even though they > have no end. Sorry. x-1<x. It's a primordial fact. Tav is not a > specific value, and neither is aleph_0. Aleph_1 is another story.... I think we accept DL's apology. So the bigulosity of N+ is not a specific value, and not a number. Yet our DL can take its square root, with the greatest of east. > Tav is a variable Bigulosity, not any kind of actual count that would > qualify as even an extended natural. Oh, it's "variable", as well as non-existent, virtually existent, non- specific, contradictory, definitely not a number. Yet another fact gleaned from recent pronouncements is that the bigulosity of N+ actually varies depending on the base the natural numbers are represented in. I suppose tav being non-existent, virtually existent, non-specific, and contradictory, it's probably not hard to make it base-dependent too. All reminds me of the filioque, somehow. This led to the Great Schism of 1054, which you will see from the Wikipedia article http://en.wikipedia.org/wiki/East-West_Schism neatly drew the boundaries for the Yugoslav civil war of recent memory. which killed around 120,000 people. As always on the side of truth, justice, and fill in the blank Brian Chandler |