Bill DeWitt <bde### [at] cflrrcom> wrote:
:     That's right, the infinte number of speres that intersect two points is
: much larger than the infinite number of circles that intersect two points.

  If we think about dimensions, then yes. With circles and two points, there's
a 1-dimensional line which is the solution to the problem. With spheres and
two points, there's 2-dimensional plane which is the solution.

  However, if we count the amount of circles and spheres, they are equal.

  Of course it's a bit odd to speak about "equal" and "bigger than" when
dealing with infinite, but it's defined in math.
  This creates some oddities. For example, there are as many natural numbers
(ie. positive integer numbers) as there are rational numbers (ie.
integer/integer). This is because each rational number can be indexed with
a pair of natural numbers.
  However, there are more real numbers than there are rational numbers.
This is because there's no way to index every real number with natural
numbers (or even rational numbers).
  This is odd knowing that given any two real numbers there will be an infinite
amount of rational numbers between them, and given any two rational numbers
there will be an infinite amount of real numbers between them. Yet there are
more real numbers than rational numbers.

-- 
#macro N(D,I)#if(I<6)cylinder{M()#local D[I]=div(D[I],104);M().5,2pigment{
rgb M()}}N(D,(D[I]>99?I:I+1))#end#end#macro M()<mod(D[I],13)-6,mod(div(D[I
],13),8)-3,10>#end blob{N(array[6]{11117333955,
7382340,3358,3900569407,970,4254934330},0)}//                     - Warp -

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