Cantor Confusion
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From: Han de Bruijn on 19 Oct 2006 03:54 imaginatorium(a)despammed.com wrote: > I expect all the non-cranks would agree with my statement, and find it > astonishing. Cranks like yourself occasionally agree with all sorts of > things, more or less by accident - so what? Cranks, cranks .. You're clearly running out of _arguments_, aren't you? Han de Bruijn
From: Han de Bruijn on 19 Oct 2006 04:03 David Marcus wrote: > You said (repeatedly) that standard mathematics contains a > contradiction, so please state the contradiction in standard > mathematics. If you use new terms, please define them. How can you state a contradiction within catholicism while adopting the standard dogmatism of that religion? As long as standard mathematics is refusing to adopt the scientific method, it can not be "contradicted". But you could try to use the other half of your brains, I mean the half that is not yet brainwashed by the standard doctrine. Han de Bruijn
From: Han de Bruijn on 19 Oct 2006 04:07 David Marcus wrote: > Dik T. Winter wrote: > >>I think that, compared to Cantor, in modern set theory potential and actual >>infinity are split up again. The contents of the set N form only a potential >>infinity, on the other hand, the *size* is an actual infinity. > > I've never seen "potential infinity" or "actual infinity" in any > textbook I've used. True. And you haven't seen any binary tree either. Han de Bruijn
From: Bob Kolker on 19 Oct 2006 05:08 Han de Bruijn wrote: > How can you state a contradiction within catholicism while adopting the > standard dogmatism of that religion? As long as standard mathematics is > refusing to adopt the scientific method, it can not be "contradicted". Mathematics done abstractly has no empirical content, so it is not a science. It is an art or discipline, but not a science. One does not test mathematical propositions the same way one tests scientific hypotheses. The are mathematical systems we know for sure are consistent since they have finite models. For example Just Plain Old Group Theory. No contradictions can be inferred from the group postulates simpliciter. Unfortunately we cannot do the same for arithmetic. Bob Kolker
From: Bob Kolker on 19 Oct 2006 05:10
Han de Bruijn wrote: > > > True. And you haven't seen any binary tree either. Bullshit. One can trivially construct finite binary trees. To "see" one is to think one. We can think binary trees as simply as we can think of a triangle with one of its sides removed. Three points, two sides. V for victory. Bob Kolker |