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From: Eckard Blumschein on 12 Apr 2005 12:42 On 4/12/2005 5:33 PM, Willy Butz wrote: In my previous > posting I forgot to mention that it is not possible > ordering cardinalities, You should add that this only refers to transfinite cardinalities. However, I guess the demand for cardinalities of finite sets will get very limited as soon as one realises that infinite numbers are just nonsense. E.
From: Eckard Blumschein on 12 Apr 2005 12:44 On 4/12/2005 5:41 PM, Torkel Franzen wrote: > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> writes: > >> Cantor was mislead by his intuition. > > No, no! He was misled by a little furry creature who twisted his > ears this way and that, and finally convinced him to gwak forth all > this nonsense about infinities. We must counter the activities > of these insidious furry creatures. We must be on our guard for > further intrusions. You did nor by chance refer to Bertrand Russel who was, according to Lavine, responsible for applying Cantor's basic idea to the reals? Eckard
From: Matt Gutting on 12 Apr 2005 12:48 Gerry Myerson wrote: > In article <vcb4qec7718.fsf(a)beta19.sm.ltu.se>, > Torkel Franzen <torkel(a)sm.luth.se> wrote: > > >>Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> writes: >> >> >>>Since it is >>>impossible to completely write down all infinitely many numerals of just >>>one single real number, it is also impossible to name its successor. >> >> The impossibility of naming the successor of a real number is indeed >>the central flaw in today's mathematics. Little can be done about it, >>I'm afraid. > > > Fortunately, no real number has ever died, so the problem > of naming a successor has not arisen. > <obvious joke> I thought that's what the cardinals were for? </obvious joke>
From: Chris Menzel on 12 Apr 2005 12:34 On Tue, 12 Apr 2005 17:42:59 +0200, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> said: > On 4/12/2005 2:00 PM, Barb Knox wrote: > >> I don't understand: here you appear to accept the distinction between >> countably and not-countably infinite, yet your main point in this >> thread seems to have been that there is only a single "oo" that >> cannot be added to or otherwise extended. How do you reconcile those >> 2 views? > > Cantor was mislead by his intuition. > I do not attribute the difference between countable and non-countable to > the size of the both infinite sets. > Actually, infinity is not a quantity but a quality that cannot be > enlarged or exhausted. So you have decided simply to use the words "countable", "uncountable", and "infinite" according to your own semantic conventions. > Whether or not an infinite set is countable depends on its structure. Sets don't have structure. What you seem to have in mind is that a set is to be considered countable or not depending on how it is *ordered*. So do you think the set of rational numbers is uncountable when ordered by the less-than relation and countable when well-ordered in some familiar fashion? > The reals are obviously not countable because one cannot even > numerically approach/identify a single real number. It's not clear what it is to "numerically approach" a number -- certainly what you say is false if we understand "approach" in terms of limits -- but could you demonstrate your thesis with regard to, say, the real number 2? Haven't I just identified it? Chris Menzel
From: Torkel Franzen on 12 Apr 2005 13:15
Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> writes: > You did nor by chance refer to Bertrand Russel who was, according to > Lavine, responsible for applying Cantor's basic idea to the reals? No, no! The furry evil creatures! Look out for them. |