Cantor Confusion
in [Math]
|
Prev: Pi berechnen: Ramanujan oder BBP
Next: Group Theory
From: Virgil on 13 Oct 2006 16:38 In article <9821b$452f5718$82a1e228$3471(a)news2.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > David Marcus wrote: > > > Han de Bruijn wrote: > > > >>Dik T. Winter wrote: > >> > >>>In article <1160647755.398538.36170(a)b28g2000cwb.googlegroups.com> > >>>mueckenh(a)rz.fh-augsburg.de writes: > >>>... > >>> > It is not > >>> > contradictory to say that in a finite set of numbers there need not be > >>> > a largest. > >>> > >>>It contradicts the definition of "finite set". But I know that you are > >>>not interested in definitions. > >> > >>Set Theory is simply not very useful. The main problem being that finite > >>sets in your axiom system are STATIC. They can not grow. Which is quite > >>contrary to common sense. (I wouldn't imagine the situation that a table > >>in a database would have to be redefined, every time when a new row has > >>to be inserted, updated or deleted ...) > > > > Is your claim only that set theory is not useful or is contrary to > > common sense? Or, are you claiming something more, e.g., that set theory > > is mathematically inconsistent? > > I said that set theory is not *very* useful. I have developed (limited) > set theoretic applications myself, so I don't say it is useless. > > Yes, a great deal of set theory is contrary to common sense. Especially > the infinitary part of it (: say cardinals, ordinals, aleph_0). > > I'm not interested in the question whether set theory is mathematically > inconsistent. What bothers me is whether it is _physically_ inconsistent > and I think - worse: I know - that it is. As set theory is entirely silent on matters of physical reality, I don't see how it can be.
From: Virgil on 13 Oct 2006 16:42 > In article <990aa$452e542e$82a1e228$16180(a)news1.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > > sqrt(-1) doesn't exist either. Frankly, I have a much harder time > believing in "imaginary" numbers than I do believing in infinite > sets. Much of electronics development over the last couple of centuries is highly dependent on the "existence" of sqrt(-1). Does HdB not believe in FM radio, TV, radar, etc.
From: Virgil on 13 Oct 2006 16:43 In article <405af$452f57ec$82a1e228$3471(a)news2.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > In article <1160675643.344464.88130(a)e3g2000cwe.googlegroups.com>, > > mueckenh(a)rz.fh-augsburg.de wrote: > > > >>With the diagonal proof you cannot show anything for infinite sets. > > > > Maybe "Mueckenh" can't but may others can. > > Define "can". > > Han de Bruijn Define "cannot".
From: Virgil on 13 Oct 2006 16:47 In article <267fc$452f5def$82a1e228$15540(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > In article <b8869$452f4a39$82a1e228$32738(a)news2.tudelft.nl>, > > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >> > >>How about: I'm not interested in "the end". I don't know where the end > >>is. And I don't care as well. As long as the end is somewhere where it > >>causes a uncertainity which is acceptable for my purpose. > > > > But what if "the end" isn't anywhere because there isn't one? > > > > As soon as you posit an end, you run into problems. You would be much > > better off saying that all such questions about an end to the naturals > > are unanswerable, and stick to what you can explicitly construct. > > Both approaches run into problems. Either you accept infinities, either > you accept a little bit of Physics: uncertainity and inexactness. Guess > you know what my choice is. Guess I know what your choice is. > > Han de Bruijn I do not object to the constraints of the mathematics of physics when doing physics, but why should I be so constrained when not doing physics?
From: Alan Morgan on 13 Oct 2006 17:30
In article <virgil-8AD47E.14423613102006(a)comcast.dca.giganews.com>, Virgil <virgil(a)comcast.net> wrote: >> In article <990aa$452e542e$82a1e228$16180(a)news1.tudelft.nl>, >> Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >> >> sqrt(-1) doesn't exist either. Frankly, I have a much harder time >> believing in "imaginary" numbers than I do believing in infinite >> sets. > >Much of electronics development over the last couple of centuries is >highly dependent on the "existence" of sqrt(-1). Does HdB not believe in >FM radio, TV, radar, etc. I was the one who said that I didn't believe in imaginary numbers, it wasn't HdB. I was trying to point out that before you have learned how they operate, imaginary numbers and infinite cardinals/ordinals don't make a lick of sense ("Waddya mean sqrt(-1)? How does that work? It's not greater than 0, less than 0, nor is it equal to 0??? How can that possibly work? You are just making stuff up!"/"Ooooh, Aleph_1! Impressive words little man. It's bigger than infinity? How can something be bigger than infinity? Infinity is bigger than everything! You are just making stuff up!"). Alan -- Defendit numerus |