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If I recall correctly, don't coordinates in 3-D and rational numbers have a higher cardinality than integers?
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yes, they do
Integers =
Rational numbers are effectively
X
Coordinates in 3D are
X
X
(for those of you who don't know, X in this case is read "cross", meaning cross product). Cross products of 2 (or more, obviously) sets are always higher cardinality than the originating sets
edit: you know what, i think this is wrong. rational numbers are the same cardinality as integers, so i guess crosses are not necessarily larger.
i can't remember about 3 dimensional coordinates.
edit2: obviously, my statement about cross products is true for finite sets