Cantor Confusion
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From: Poker Joker on 30 Sep 2006 00:49 "MoeBlee" <jazzmobe(a)hotmail.com> wrote in message news:1159581865.120392.117490(a)h48g2000cwc.googlegroups.com... > Like I said, you've not refuted the uncountability of the reals nor > Arturo's point to which you originally responded. I never tried to refute the uncountability of the reals. Too bad you've never been able to understand that. I don't need to respond to you about Arturo.
From: Poker Joker on 30 Sep 2006 00:50 "Virgil" <virgil(a)comcast.net> wrote in message news:virgil-733334.21102929092006(a)comcast.dca.giganews.com... > In article <_YjTg.25592$QT.21259(a)tornado.rdc-kc.rr.com>, > "Poker Joker" <Poker(a)wi.rr.com> wrote: > > >> I understand everything you understand. I just understand more, and >> that confuses you. > > Joker seems to have delusions of competency. Virgil *IS* delusional. I love it when mathematicians and Virgil start to act like babies.
From: Poker Joker on 30 Sep 2006 00:52 "Virgil" <virgil(a)comcast.net> wrote in message news:virgil-B92CDB.20515029092006(a)comcast.dca.giganews.com... >> By analogy, what you're saying is: >> >> For ANY x >> there is a procedure to find a y such that x/y = 1. >> >> Because we are using the verbage "ANY", we don't >> have to worry about special cases like when x = 0. >> That's how mathematicians work? > > Except that mathematicians can't prove "any" when there are > counterexamples. And mathematicians can prove "any" in the list of reals > case. You should let mathematicians speak for themselves. You should stick to name-calling and acting like a baby. >> Or are you just saying that you need not look at special >> cases when we don't want to? Or is it that if a special >> case is overlooked enough, then it no longer counts? > > I am saying that when one can prove something for "any" case then > special cases are irrelevant. Just stick to acting like a three-year-old. You're much better at it.
From: Virgil on 30 Sep 2006 02:44 In article <451dddd9(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > > > > The original proof was regarding a complete language using > at least two symbols, m and w, no? Not quite. Two disjoint sets of synbols. > That was later conflated to a proof about the reals. It was later shown that it could be modified to form a proof that the set of all reals is uncountable.
From: Virgil on 30 Sep 2006 02:53
In article <451dde36(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > William Hughes wrote: > > > > In this case > > the proof goes > > > > 1 Let A be a list > > 2 Use D to contruct a real number r > > 3 Show that r in not an element of A > > 4 Conclude that A does not contain all the > > real numbers > > > > Again, since D can be applied to any list > > step 2 is valid. > > > > - William Hughes > > > > This list must be in representation using 2 or more symbols, yes? Slightly misleading, since 2 symbols are not enough. For the reals one must have at least 4 symbols to avoid problems with the dual representations of certain rationals which have both a terminating form and a non-terminating eventually repeating form. if it were not for those dual representations, 2 symbols would suffice. |