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The fourth part of Hilbert's hotel paradox, on rational numbers and reals.
Part One:
http://www.youtube.com/watch?v=SLHiq7...
Part Two:
http://www.youtube.com/watch?v=_Dgro9...
Part Three:
http://www.youtube.com/watch?v=BSwpVE...
Part Four:
http://www.youtube.com/watch?v=XVSqPs...
Part Five:
http://www.youtube.com/watch?v=zectsb...