The Definition of Points
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From: Bob Kolker on 1 Apr 2007 07:11 T. O wrote. > One may express them algebraically, but their truth is derived and > justified geometrically. There is only one justification in mathematics. Does the conclusion follow logically from the premises. Bob Kolker
From: Bob Kolker on 1 Apr 2007 07:12 Tony Orlow wrote:> > That is like saying your mind has outgrown your body, so you no longer > need to eat or breathe. The language of math is the more abstract > aspect, but the geometry of it is still the basis of its truth. So it counting. Bob Kolker
From: Bob Kolker on 1 Apr 2007 07:12 Tony Orlow wrote: > > That is like saying your mind has outgrown your body, so you no longer > need to eat or breathe. The language of math is the more abstract > aspect, but the geometry of it is still the basis of its truth. So is counting. Bob Kolker
From: Bob Kolker on 1 Apr 2007 07:14 Tony Orlow wrote: > > > Bob - wake up. How do we know relativity is correct? Because it follows > from e=mc^2? Correct in what sense. Mathematically, relativity theory is simply an excercise in Poincare groups. As a physics theory, we insist on empirical corroberation of the conclusions that are interpreted to say something about the world. Bob Kolker
From: Bob Kolker on 1 Apr 2007 07:20
Tony Orlow wrote: > As I said to Brian, it's provably the size of the set of finite natural > numbers greater than or equal to 1. No, there is no last finite natural, > and no, there is no "size" for N. Aleph_0 is a phantom. What about the class of all sets that can be put in correspondence with the set of intergers with a 1-1 onto mapping. That is what cardinality is. It is an equivalence class of sets under the relationship of equinumerosity. Bob Kolker |