>>> Bob Sewell on Infinity 
 
 BS> infinity + infinity = infinity = infinity ^ 2 = infinity ^ infinity,
No!!!  2^infinity > infinity.  A diagonal argument can prove this.  Are you 
familiar with set theory?  Otherwise a digital proof can be made for 
denumerable (countable) infinity.  Namely that there are -more- real numbers 
than rational numbers.  Hence a -larger- non-denumerable or uncountable 
infinity in addition to the smaller denumerable or countable infinity.
 BS> This is what I mean, and maybe this is all the proof you'll need.
 BS> In any case, it shows you what countably infinite means and gives a
 BS> visual image of my proof to go with the one I referred you to.
 BS> Positive Integers:  1  2  3  4  5  6  7  8  9  10  11  12  13  ...
 BS> All Integers:  0  1 -1  2 -2  3 -3  4 -4   5  -5   6  -6  ...
 BS> Even Integers:  0  2  4  6  8 10 12 14 16  18  20  22  24  ...
Basically your proof corresponds x with 2 * x or x/2, so this proof would 
apply to uncountable as well as to countable infinity.  As for showing 
infinity^2 = infinity, a different correspondence is needed.  For countable, 
a diagonal enumeration suffices.  Hence rational numbers and integers are 
equi-numerous.  But to show that the plane and line are equinumerous is more 
difficult as there is no continuous mapping between the two.
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