Cantor Confusion
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From: Eckard Blumschein on 1 Dec 2006 05:42 On 11/30/2006 1:39 PM, Bob Kolker wrote: > Eckard Blumschein wrote: >> >> >> Large enough is certainly not qualitatively different enough, infinity >> is the location where two parallel lines are thought to meet each other, >> and division by zero has been forbidden because it yields anything. > > Division by zero in a field yeilds a contradiction. Just this contradiction resides already in the notion of (actual) infinity. The task division by zero cannot be performed. It would require to leave the realm of numbers. > > 1/0 = x (for some x in the field) implies 1 = 0*x = 0. That simply will > not do. Likewise oo + a = oo seems to imply a = oo - oo = 0. Isn't it better to understand why it is incorrect than simply to learn it is forbidden? Eckard Blumschein
From: mueckenh on 1 Dec 2006 06:33 MoeBlee schrieb: > > > There is nothing in that that shows that a set is not a fixed entity. > > > > The universe of all sets can grow. Define: "The universe of all sets is > > called the set of all sets", and you see it. > > As to what Fraenkel, Bar-Hillel, and Levy wrote, they are underscoring > the fact that different axioms yield different universes of sets. That > is what they mean by the universe of sets "growing" (scare quotes in > original text). You should try to distinguish between "to differ" and "to grow". You may scream as loud as you can. These verbs are different and denote different processes. > > An easy example which > > should not escape you: The set of states of the EC has been growing and > > probably will continue to grow. > > Which you'll have a hard time proving to be a set in Z set theory. Of course in set theory there are variables denoting sets. In any book on ZF set theory you can find sentences like: "The letters X and Y in these expressions are variables; they stand for (denote) unspecified, arbitrary sets." By such tools it is very easy to deal with a set like the set of states of the EC in ZF. It turns out again and again that you have very little knowledge about set theory and its philosophy. I am sorry but as your behaviour parallels your expertise I will no longer discuss with you. A last hint may help you to become a decent person and socialize with your surrounding: You should know that it is not appropriate to speak out everything one thinks. In general it is not useful to injure persons. What would it help if I publicly uttered what I think of you? Last regards, WM
From: Bob Kolker on 1 Dec 2006 06:51 Eckard Blumschein wrote: > > Once again: > _Sentences_ _containing_ _unlimited_ _quantifiers_ _are_ _in_ _general_ > _meaningless_" Nonesense! Unsinn! (x)(T(x) -> P(x)) T(x) means x is a tree, P(x) means x is a plant and -> is implies. The above statement is true, meaningful and contains unlimited quantifiers. EB, you are such an incompetent. Why not take up basket weaving or tiddlywinks. Forget about mathematics. You simply don't have the brains for it.. Bob Kolker
From: Bob Kolker on 1 Dec 2006 06:52 Eckard Blumschein wrote: > On 11/30/2006 1:38 PM, Bob Kolker wrote: > >>Eckard Blumschein wrote: >> >> >>>Really? Fraenkel, 2nd ed. 1923, approved Cantor having managed not just >>>to battle but also refute an assertion by Gauss. >>>Is there any evidence for this proud claim? No. >>>Whenever Cantor declared mathematicians like Aristotele, Locke, >> >>Locke and Aristotle were NOT mathematicians. Aristotle was at most, a >>logician or an ethicist or a political "scientist" or a literarary critic. >> >>As a scientist he was a failure. Why? He didn't check. >> >>Bob Kolker > > > Weren't Aristotele, Galilei, Newton, Leibniz, Locke, Spinoza, Peirce, > Poincar�, Einstein, Weyl so called universal scientists? Spinoza was a lens grinder and a philosopher. He did not do mathematics. > Fermat who paved the way for calculus was not a mathematician but a > lawyer. Borel was a politician. > You are perhaps a mathematician. Do you believe to understand > mathematics deeper than one out of the mentioned? > > Why should mathematics be esoteric? It isn't. Bob Kolker
From: Bob Kolker on 1 Dec 2006 06:53
Eckard Blumschein wrote: > > > Likewise oo + a = oo seems to imply a = oo - oo = 0. oo is not a number. Once again you show you simply do not understand mathematics. Bob Kolker |