I once did something like this myself, and came up with this interesting
thought:

let's say you placed a point (sphere with radius zero) on every integral
point in 3D space. (like, at the origin, and at <1,0,0>, and at <-2,1,0>,
and at <4052,153,398>, you get the idea), so you have an infinite 3D grid of
points. Now, you remove the point at the origin and place yourself there.

Is it possible to look in any direction without seeing a point? (meaning,
can you shoot a ray out from the origin that doesn't intersect a point on
the grid?)

 - Slime
[ http://www.slimeland.com/ ]

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