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 
times, where 
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.
Thomson Lamp Paradox
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References
Erickson, G. W. and Fossa, J. A. Dictionary of Paradox. Lanham, MD: University Press of America, pp. 106-107, 1998.Pickover, C. A. Keys to Infinity. New York: Wiley, pp. 19-23, 1995.Cite this as:
Weisstein, Eric W. "Thomson Lamp Paradox." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ThomsonLampParadox.html