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   From: morpheal@sympatico.ca   
      
   Sylvia Else wrote:   
   >   
   > _Schwann_ wrote:   
   >   
   > > That's news to me. I thought infinity meant infinite, which means that   
   > > it can be ascribed a symbol, but not a number. I suppose, like most   
   > > else, it depends how it was 'meant' and I meant 'infinite, without   
   > > number or end...   
   > >   
   > > thanks for the interesting comment....   
   >   
   > An example of a countable infinity is the set of rational numbers. You   
   > can write them all down this way   
   >   
   > 1/1 2/1 3/1 4/1 5/1 ...   
   >   
   > 1/2 2/2 3/2 4/2 5/2 ...   
   >   
   > 1/3 2/3 3/3 4/3 5/3 ...   
   >   
   > 1/4 2/4 3/4 4/4 5/4 ...   
   >   
   > 1/5 2/5 3/5 4/5 5/5 ...   
   >   
   > etc.   
   >   
   > Now you take ever larger diagonal sweeps through them   
   >   
   > 1/1  1/2 2/1  1/3 2/2 3/1  1/4 2/3 3/2 4/1  1/5 2/4 3/3 4/2 5/1 ...   
   >   
   > So there's a systematic way of putting them into a list, and you can   
   > count them in the sense that you can assign an integer to each of them   
   >   
   > 1  1/1   
   > 2  1/2   
   > 3  2/1   
   > 4  1/3   
   > 5  2/2   
   > 6  3/1   
   > 7  1/4   
   > 8  2/3   
   > 9  3/2   
   > 10 4/1   
   > 11 1/5   
   > 12 2/4   
   > 13 3/3   
   > 14 4/2   
   > 15 5/1   
   >   
   > etc.   
   >   
   > OK - big deal.   
   >   
   > But try it with all numbers, including the irrational ones. Suppose we   
   > wrote their decimal expansions down in a list, like this. Some end with   
   > a (countably) infinite number of zeros, but most don't.   
   >   
   > 1  abcdef.....   
   > 2  ghijkl.....   
   > 3  zyxwv......   
   > 4  mnopq......   
   >   
   > where the letters stand for arbitrary digits (not necessarily different).   
   >   
   > Now, write a number whose first digit is not the first digit of the   
   > first number (ie, not a), whose second digit is not the second digit of   
   > the second number (ie, not h), and so on.   
   >   
   > Since it has at least one digit that differs from the corresponding   
   > digit of a number in the list, our constructed number cannot be in the   
   > list, despite the list supposedly containing all the numbers.   
   >   
   > The conlusion must be that it is not possible to write down all the   
   > numbers in a list, even if the list is infinitely long. This is an   
   > uncountable infinity.   
   >   
   > Sylvia.   
      
      
   No. No. No. Arrrgh..... No.   
      
   In mythematics (mathematics to some who still believe that that language   
   describes all and everything completely accurately) infinity is simply   
   an incalculable. There are many reasons why you cannot calculate   
   something, but there you have it it is infinite.   
      
   That isn't absolute infinity. Absolute infinity is really really   
   infinite and not simply mythematical.   
      
   As for time, you would have to be able to handle coordinates plotted in   
   five irreducable dimensions to get even a start at it.  Try to draw that   
   on a piece of paper the way you would 3 or attempt to draw 4. Now make   
   it 5 so that they all work together. Good luck. You have to be able to   
   plot your course using that.... time traveller.   
      
   Then you take that and multiply it by the number of branching paths,   
   according to bifurcations of quantum destinies, to allow for your five   
   dimensional system being doubled, tripled, quadrupled, etc. Oh, yes, the   
   five and five and five and more fives can overlap, coincide, and do all   
   sorts of wonderful things to mess you up.   
      
   What you see if never what you get.   
      
   R.M.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)