Uncountability of the Rationals?
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From: Tony Orlow on 11 Jun 2010 09:48 On Jun 10, 11:35 pm, David R Tribble <da...(a)tribble.com> wrote: > MoeBlee wrote: > >> MoeBlee: So you can't compare the airplane, which > >> accomplishes a certain purpose, with your ball, which does not > >> accomplish that purpose. > >> ToeKnee: You just don't get it. Sigh. > >> ChanceFor PrinceOfPull: There goes MoeBlee again silencing alternative > >> theories. > > Transfer Principle (L Walker) wrote: > > > [...] In this analogy, > > MoeBlee is forcing everyone to fly only on American > > Airlines and not Virgin or any other airline. > > I like to believe that a wonderful theory can come out > > of allowing proper subsets to have distinct sizes, but > > MoeBlee won't even let us _build_ the plane, much less > > fly it anywhere. > > Bad, bad, naughty MoeBlee, preventing you from considering > other theories like that. > > Sorry, but how exactly is he forcing you to use only ZFC? > Perhaps you have some secret knowledge about MoeBlee's hidden > powers over the Internet, as but far as the rest of us are concerned, > this is a free forum for suggesting new ideas. > > It's Tony who keeps claiming that his bigulosity, T-riffics, IFC, and > all the rest fit well within (or as simple extensions of) standard > theory, > in spite of all continuing evidence to the contrary. I never claimed any such thing. My ideas are clearly at odds with transfinite set theory. I make no apologies for that, nor should I be expected to. Please don't misrepresent my position. Thanks you for your time and attention. Sarcastically yours, TOny > > Since you're so quick to defend Tony's ideas from sinister forces > like MoeBlee, it's apparent that you possess a deeper understanding > of them than the rest of us. So perhaps you can elucidate these > ideas in a more formal way, since Tony seems to be having such > a problem doing that?
From: Tony Orlow on 11 Jun 2010 09:51 On Jun 10, 11:48 pm, David R Tribble <da...(a)tribble.com> wrote: > Tony Orlow wrote: > > Hi Transfer - > > I was wondering what thoughts you had on the countably infinitely long > > complete list of digital strings, if anything. > > That would be the countable list of all finite-length digital strings, > wouldn't it? Or would it be the uncountable list of all infinite- > length > digital strings? > > There's a simple test to tell the difference between the two. > The finite digital string .3 (or if you like, its equivalent "value" > string, 0.3000...) exists in the first (countable) list; the > infinite digital string .333... exists in the second (uncountable) > list. > > The second test is to find the successor (or, if you prefer, the > predecessor) to each of those strings within their lists. Um, excuse me, but is the list of all finite digital strings not ultimately countably infinite in width? If it is finite, then please state this finite width. If it is countably infinite, then how does it differ from your uncountably long list? Tony
From: Tony Orlow on 11 Jun 2010 09:53 On Jun 11, 12:07 am, Brian Chandler <imaginator...(a)despammed.com> wrote: > David R Tribble wrote: > > > Tony Orlow wrote: > > > Yes. > > > E 0 > > > E 1 > > > 0<1 > > > x<y -> E z: x<z<y > > > > This leads to some level of infinites between counting numbers. > > > That's hard to believe. The only thing that your definitions do > > is define two numbers, 0 and 1, and an order relation for them. > > Where are all of the rest of the reals? Or even the naturals? > > Well, his last line seems to say that there is also z, such that 0 < z > < 1. For example, the binary fractions would surely fit his > definition. > > Brian Chandler Thank you. Of course, the fact there there exists a z between any x and y such that x<y doesn't imply that z necessarily is equal to (x+y)/ 2, so this general statement really just leads to a dense set, of which the binary fractions are only one example. Peace, TOny
From: Tony Orlow on 11 Jun 2010 09:55 On Jun 11, 12:21 am, David R Tribble <da...(a)tribble.com> wrote: > Tony Orlow wrote: > > For, "none > > shall drive us from the Garden which Cantor has created for us". If it > > doesn't produce fruit, it's time to plant a new bed, or at least > > fertilize. > > Well, it's done pretty well for the last 100+ years. Have any > of your ideas produced any results of consequence yet? > > I'm still waiting to hear what bigulosity/IFR says about the size > of the set of natural squares. Any results yet? I already did that. According to IFR it's sqrt(omega), which according to ICI is less than omega. Tony
From: Tony Orlow on 11 Jun 2010 09:58
On Jun 11, 12:33 am, David R Tribble <da...(a)tribble.com> wrote: > David R Tribble writes: > >> So then what is the *general* case for IFR? > > Jesse F. Hughes wrote: > > Could someone remind me what IFR stands for? > > I don't remember what Tony's "IFR" stands for, either. Something > about a "formulaic ratio" or some such. > > The funny thing about this is that this does not seem to matter > in the least. Tony keeps saying that IFR solves all sorts of > problems and "obfuscations" with Cantor's cardinalities, yet > he hasn't given a single concrete example of it. So, you can't even remember what it stands for or what it means, but you are sure it's incosistent. Well, I've never tried eating hippo meat, but I don't like it. I just know I don't like it because it's not a hamburger. I mean, come on. If you don't understand it how can you criticize it? By the way, the statetment that "he hasn't given a single concrete example of it" is not merely disingenuous, but an outright lie, and you know it. Tony |