Uncountability of the Rationals?
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From: FredJeffries on 12 Jun 2010 15:47 On Jun 12, 12:42 pm, David R Tribble <da...(a)tribble.com> wrote: > Jesse F. Hughes wrote: > >> You [Tony] sometimes say that you > >> don't think omega is the smallest infinite ordinal, but I'm not sure > >> what you mean when you say that. > > Tony Orlow wrote: > > I don't use the word "ordinal" in my arguments (sure, go find one > > mention from 1996 or whatever). I say there are a wide spectrum of > > countable and uncountable infiniites, given the right techniques. > > What Tony means is that size(E) < size(N) for the sets N and > E = {0,2,4,6,...}. Specifically, he means that size(E) = size(N)/2, > where "size(S)" is his personal definition of "set size". No, he told me that Size(E) = Size(N)/2 + 1 http://groups.google.com/group/sci.math/msg/df77005159c91c90 because of 0. At least, I THINK that's what he told me. > > He also allows for things like sqrt(size(N)) and log(size(R)). > These "values" of his are "different infinities", all based on his > idea of a "unit infinity".
From: David R Tribble on 12 Jun 2010 16:02 Tony Orlow wrote: > ELiminating proper subset equinumerosity is worthwhile. That kind of statement hints at a deep misunderstanding of the way mathematics works. You seem to be suggesting that by inventing an alternative way of measuring set sizes (a more "intuitive" way), that the existence of bijections between infinite sets and their proper infinite subsets will disappear or stop working. Unless you invent a system of "sets" that flat out does not allow relations like injections and surjections to be formulated at all, you can't do this. Either that or come up with a system having completely different meanings for "subset" and "mapping".
From: David R Tribble on 12 Jun 2010 16:18 Tony Orlow writes: >> PS - If you wouldn't mind laying off, the JSH references get a tad tiring. > Jesse F. Hughes wrote: > I never overrule the random sig picker. > > -- > "People make mistakes. Better to live today and learn the truth, than > to be one of those poor saps who died deluded, thinking they knew > certain things that they just didn't. Thinking they had proofs that > they didn't." --James S. Harris, almost too sad for a .sig Wow. Your sig picker must be psychic, or perhaps artificially intelligent. -- The dash-dash your eyes just passed over indicates that the content of this message has terminated, and that any text following it is bound to be irrelevant, whether or not it is humorous, insightful, or derogatory. -drt
From: Marshall on 12 Jun 2010 18:27 On Jun 12, 1:18 pm, David R Tribble <da...(a)tribble.com> wrote: > Tony Orlow writes: > >> PS - If you wouldn't mind laying off, the JSH references get a tad tiring. > > Jesse F. Hughes wrote: > > I never overrule the random sig picker. > > > -- > > "People make mistakes. Better to live today and learn the truth, than > > to be one of those poor saps who died deluded, thinking they knew > > certain things that they just didn't. Thinking they had proofs that > > they didn't." --James S. Harris, almost too sad for a .sig > > Wow. Your sig picker must be psychic, or perhaps artificially > intelligent. It demonstrates its relevance via the same mechanism that Herc uses when pointing to random pages in a book. Marshall
From: David R Tribble on 12 Jun 2010 19:27
Jesse F. Hughes wrote: >> You [Tony] sometimes say that you >> don't think omega is the smallest infinite ordinal, but I'm not sure >> what you mean when you say that. > Tony Orlow wrote: >> I don't use the word "ordinal" in my arguments (sure, go find one >> mention from 1996 or whatever). I say there are a wide spectrum of >> countable and uncountable infiniites, given the right techniques. > David R Tribble wrote: >> What Tony means is that size(E) < size(N) for the sets N and >> E = {0,2,4,6,...}. Specifically, he means that size(E) = size(N)/2, >> where "size(S)" is his personal definition of "set size". > Fred Jeffries wrote: > No, he told me that Size(E) = Size(N)/2 + 1 > http://groups.google.com/group/sci.math/msg/df77005159c91c90 > because of 0. Actually, I think he said that size(E) = size(N)/2 +1 *and* that size(E) = size(N)/2 + 1/2. |