Cantor Confusion
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From: Virgil on 18 Nov 2006 16:23 In article <MPG.1fc90ff92e8ec01d989922(a)news.rcn.com>, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > mueckenh(a)rz.fh-augsburg.de wrote: > > David Marcus schrieb: > > > > > If an actually infinite set of numbers existed, and if neighbouring > > > > elements had a fixed distance from each other, then the set must > > > > contain an infinite number. > > > > > Is that a "no" or a "yes"? > > > > Read again, simplified: If neighbouring elements have a fixed distance, > > the answer is yes. > > If neighbouring elements have not a fixed distance like the rational > > numbers: the answer is no > > Let's try a simpler question: > > Does an actually infinite set exist? WM has already committed himself to a situation in which as set like the rationals need not contain any "infinite element" but that a proper subset of it, like the integral rationals, must contain an "infinite element". One wonders how a proper subset can contain an element not in the containing superset?
From: stephen on 18 Nov 2006 16:29 David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > stephen(a)nomail.com wrote: >> David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >> > Lester Zick wrote: >> >> On Thu, 16 Nov 2006 02:02:49 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >> >> >Please give a specific example of something that you think is absurd or >> >> >a contradiction. I don't know what you mean by "containment of sets and >> >> >subsets". >> >> >> >> Well as I recollect Stephen seems to think infinite sets are proper >> >> subsets of themselves. >> >> > Are you sure that is what Stephen thinks? >> >> I see Lester has resorted to lying. This is all part of his >> standard pattern. He really is pathetic. It is amusing to see >> how increasingly pathetic he becomes. > And, such a silly lie. What could he hope to gain? I am not sure if it is really even just a lie. Honestly I do not think Lester is capable of comprehending anything mathematical, so when he tries to restate what anybody else has said he gets it wrong not just because of dishonesty (he has clearly demonstrated a decided dishonest streak), but because of ineptitude. When he reads something like "A set is infinite if there exists a bijection between itself and a proper subset." all that comes through is "* set is infinite ** ***** ****** * ********* ****** itself *** * proper subset." and that is somehow boiled down into "An infinite set is a proper subset of itself". It reminds me of this: http://www.bakbone.com/newsletter/images/ginger_large.gif Stephen
From: Virgil on 18 Nov 2006 16:54 In article <MPG.1fc939f0d3c5ef9e989935(a)news.rcn.com>, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > stephen(a)nomail.com wrote: > > David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > > > Lester Zick wrote: > > >> On Thu, 16 Nov 2006 02:02:49 -0500, David Marcus > > >> <DavidMarcus(a)alumdotmit.edu> wrote: > > >> >Please give a specific example of something that you think is absurd or > > >> >a contradiction. I don't know what you mean by "containment of sets and > > >> >subsets". > > >> > > >> Well as I recollect Stephen seems to think infinite sets are proper > > >> subsets of themselves. > > > > > Are you sure that is what Stephen thinks? > > > > I see Lester has resorted to lying. This is all part of his > > standard pattern. He really is pathetic. It is amusing to see > > how increasingly pathetic he becomes. > > And, such a silly lie. What could he hope to gain? Attention!
From: Virgil on 18 Nov 2006 16:55 In article <MPG.1fc93be371a2a1d0989936(a)news.rcn.com>, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > Virgil wrote: > > WM again has cart-before-horse-itis. > > He thinks he doesn't need a horse. He does need the other half to be a complete horse.
From: David Marcus on 18 Nov 2006 20:19
stephen(a)nomail.com wrote: > David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > > And, such a silly lie. What could he hope to gain? > > I am not sure if it is really even just a lie. Honestly I do not > think Lester is capable of comprehending anything mathematical, > so when he tries to restate what anybody else has said he > gets it wrong not just because of dishonesty (he has > clearly demonstrated a decided dishonest streak), but because of > ineptitude. When he reads something like > "A set is infinite if there exists a bijection between itself > and a proper subset." > all that comes through is > "* set is infinite ** ***** ****** * ********* ****** itself > *** * proper subset." > and that is somehow boiled down into "An infinite set is a proper subset > of itself". It reminds me of this: > http://www.bakbone.com/newsletter/images/ginger_large.gif Could be. It could also be that Lester thinks it is all nonsense, so he doesn't care whether he says exactly what the person says. -- David Marcus |