Galileo's Paradox
in [Math]
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From: Eckard Blumschein on 30 Nov 2006 07:09 On 11/29/2006 8:21 PM, Virgil wrote: > Does volume completely determine mass? Different measures measure > different things and need have any correlation. Since measure theory is mathematics, it should be in position to abstract from physics and have only one measure for let's say seven eleven.
From: Bob Kolker on 30 Nov 2006 07:32 Eckard Blumschein wrote: > > Uncountable means: Counting is impossible. This property obviously > belongs to fictitious elements of continuum. There is simply too much of > them. So counting is not feasible. As long as one looks at a finite, > just potentially infinite heap of single integers, one has to do with > individuals. The set of all integers is something else. It is a fiction. > It is to be thought constituted of an uncountable amount of > non-elementary elements. Well this looks nonsensical. There is indeed a > selfcontradiction within the notion of an infinite set. > Non-elementary means not having a distinct numerical address. Element > means "exactly defined by an impossible task". Have you forgotten to take your meds again? Bob Kolker
From: Bob Kolker on 30 Nov 2006 07:32 Eckard Blumschein wrote: > > > I consider Dedekind wrong, and he admitted to have no evidence in order > to justify his basic idea. What sort of evidence? Surely not empirical evidence. Mathematics done abstractly has no empirical content whatsoever. Bob Kolker >
From: Bob Kolker on 30 Nov 2006 07:34 Tonico wrote: > Ps Have you, and anyone else, noted how all the anticantorian cranks > are NEVER mathematicians? But Internet welcomes all, and google's > sci.math is an uncensored group, so anyone can offer his piece to > all...and you know what? I think this is just fine. I'm convinced that > also from the most stupid, dense and even annoying crank/troll we all > can learn. That does seem to be the case. Mathematicians stopped kicking about the Cantorian approach many decades ago. Giants, such as Hilbert, welcomed Cantorian mathematics. Bob Kolker
From: Eckard Blumschein on 30 Nov 2006 09:46
On 11/30/2006 4:41 AM, zuhair wrote: > Six wrote: >> 2) It makes no sense to compare infinite sets for size, neither to say one >> is bigger than the other, nor to say one is the same size as another. The >> infinite is just infinite. > > Yea, a quite negative approach. But it is not without intuitive > backround. Intuitivelly speaking the idea that an infinite set has no > fixed size comes to ones mind. That idea that infinity makes all > infinite sets equal in size is also beautiful, Really? The OP did not write equal in size. Infinite is just infinite but no size. > and I think it was the > idea before Cantor showed that there can be infinite sets of different > sizes, He did not! Not! Not! He just misinterpreted uncountable as mor than countable. Is incorrect more than correct? > the alephes and the powers are different in size, though > infinite. If you want to change the definition of infinity to a one > like saying, infinity is that quality which cause all sets that possess > it to be equal in size, instead of the current definition of an > infinite set, that is a set injectable to some proper subset of it, > then you are free to do that,provided you bring a new definition of set > size, other than cardinality. But this definition that looks to be > their in your mind, is a negative one, I mean it canceal the chance of > having meaningful comparisons of sizes of sets when they are infinite. The idea of considering sets was born in order to make the illusion by Dedekind and Cantor less obviously wrong than it was with numbers. > If you bring a more positive claim, The argument Cantors transfinite numbers are somthing positive something progressive is old and has proven wrong. Not even aleph_2 has found an application. |