Thomson's lamp

Thomson's lamp is a philosophical puzzle based on infinites.

It was devised in 1954 by British philosopher James F. Thomson, who used it to analyze the possibility of a supertask, which is the completion of an infinite number of tasks.

Now suppose that there is a being who is able to perform the following task: starting a timer, he turns the lamp on.

[1] Thomson reasoned that this supertask creates a contradiction: It seems impossible to answer this question.

In other words, as n takes the values of each of the non-negative integers 0, 1, 2, 3, ... in turn, the series generates the sequence {1, 0, 1, 0, ...}, representing the changing state of the lamp.

One of Thomson's objectives in his original 1954 paper is to differentiate supertasks from their series analogies.