** Is the Light On or Off? **

Suppose a light is switched on for a half-minute, off for a quarter minute, on for one eighth of a minute and so on until precisely one minute has elapsed. Is the light on or off at the end of this (infinite) process? Representing the two states “on” and “off” by and , the sequence of states over the first minute is . But how do we ascertain the final state from this sequence? This question is sometimes known as Thomson’s Lamp Puzzle.