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How big is infinity?
There is a whole book on this topic. "Infinity and the Mind: The Science and Philosophy of the Infinite" by Rudy Rucker. It explains all the different types of infinities in mathematics. Quite an intimidating read for the non-mathematicians, though.
Find third 3d coordinate given two other coordinates
The point which I wanted add is : For the above solution to work the line joining the center of the green and blue sphere has to be parallel to the box. This is not specified explicitly in the question.