Define: Thomsom lamp from mathemati....

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Define: Thomsom lamp

Back (Answer)

Suppose you have a reading lamp with a push-button that switches the light on and off. If the light is "off" when you press the button once, or any odd number of times, the lamp will be "on". Press it any number of even times and it will be "off". A little demon appears and decides he will press the button continually so as to leave the lamp 'on' for 1/2 a minute, then 'off' for 1/4 a minute, 'on' for 1/8 of a minute, 'off' for 1/16 of a minute and so on. He will have pressed the button an infinite number of times after 1 minute. So the big question is: Will the light be 'on' or 'off' after one minute.

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