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Posted by markr on 24/10/2009, 8:53 am, in reply to "query/proposition"
I'm having a tough time visualizing that, but how does this work for you?
You've got an infinite number of objects that are all the same shape. That shape is an infinitely long piece of 2x4 lumber with 1" holes cut every foot. But, in one location, instead of a hole, there is an infinitely long 1" diameter dowel extending in one direction orthogonal to the 2x4 and parallel to the axes of the holes. It would be easy to build a miniature finite model.
These can now be stacked infinitely high in such a way that the dowel of the next piece to be placed is one foot to the right of the dowel of the previously placed piece. It is clear that each piece touches each piece above it via its dowel, and is touched by each piece below it by that piece's dowel.
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