Thomson Lamp Paradox

A lamp is turned on for 1/2 minute, off for 1/4 minute, on for 1/8 minute, etc. At the end of one minute, the lamp switch will have been moved $\aleph_0$ times, where $\aleph_0$ is Aleph-0. Will the lamp be on or off? This Paradox is actually nonsensical, since it is equivalent to asking if the ``last'' Integer is Even or Odd.

References

Pickover, C. A. Keys to Infinity. New York: Wiley, pp. 19-23, 1995.