>
>Matt Eggleston wrote to Bob Sewell about "Existence Exists"
 ME> Which means you cannot derive the infinite from the finite.
 ME> GIVEN: Math only describes something if there has been a thing
 ME> observed acting in the manner which the math describes.
 ME> GIVEN: Nothing has been observed being infinite.
 ME> QED:   There is nothing which is mathematically infinite.
 ME> That was an amazingly simple proof.
 Simple, and wrong.  You give as your first premise that Math only
 describes something if there has been a thing observed acting in the
 manner which the math describes.  This requires, first, a "thing" -
 which is concrete and observable.  Math describes the unobserved, 
 the abstract, it does not depend upon concrete things, or observation.
 
 An excellent example would be this infinite-radical problem.
 
 EVALUATE
        -----------------------------------------------------
       |            -----------------------------------------
       |            |           ----------------------------- 
       |   1+2      |          |
       |            |   1+3    |
   \   |        \   |          |   1+ ...
    \  |         \  |      \   |
     \ |          \ |       \  |
      \|           \|        \ |
                              \|
                              
 There is a finite answer, and it _can_ be _proved_.  But even though it
 must be carried out forever and ever and ever - it can still be solved.
 And is solved.  
 
 The proof is rather long, but:
 
         -------------------------------------------------------------
        |                     --------------------------------------
        |                    |                            ---------- 
 x+n+a= | ax+((n+a)*(n+a))+x | a(x+n)+((n+a)*(n+a))+(x+n) | (etc)
        |                    |                            |
    \   |                    |                            |    
     \  |                 \  |                        \   |
      \ |                  \ |                         \  |
       \|                   \|                          \ |
                                                         \|
 
  Break down any number, 3 for example, into x, n, and a, such that x=1,
  n=2, and a=0.  The answer then is always going to be 3.  
  
  Many kinds of mathematical processes can be ordered to proceed ad
  infinitum.  Nested radicals (such as the above example),  continued
  fractions, and infinite series, among many myriads of other examples,
  perhaps infinite examples.
  
  Please note this infinite series, for example:
  
  1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + ...
  
  Add this forever.  
  What do you get?  
  
  You get very very close to 2, but you never quite get there.  But you
  get "close enough", yet you never get there anyway.  Not even after an 
  infinite number of additions.  Please, try it and see.  It should occupy
  you for the next 10^1000 quadrillenion millenia of eons.  ;-)
  
  So, please: spare me your "proof" that there is nothing which is
  mathematically infinite.  We may have to use three dots to get the
  idea across - but its existence is _real_ - even if it does reside
  in the consciousness alone.  
... For the millionth time, don't exaggerate!
--- GEcho 1.11++TAG 2.7c
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