At the end of the day, he would still be staring at the same blank sheet of paper.

Did it ever happen to you that you would sit to try to solve a new problem, and the more you would think about it the less it would make sense to you? if you would do that at your desk, would you then be considered non-productive? if you were a game developer be it technical, artistic or manager, sitting there and not typing for hours without making any progress would that be bad? well, Bertrand Russell, one of the most famous logicians of all times did exactly that, so you are ok :)


S = {x : x is a set and x !∈ x}.
In other words, S is the set of all sets that do not contain themselves.

In more 'naive' words:

* In Seville, there’s a barber who shaves all those people who do not shave themselves. Does the
barber shave himself or not? This is known as the “Barber of Seville problem”.

* Imagine a card. On one side is written, “The statement on the other side of this card is true.” and
on the other side is written, “The statement on the other side of this card is false.”

Bertrand Russell, one of the most famous logicians ever, struggled with this problem for a long time. In his autobiography, he describes just how hard he found the problem. Every morning, he said, he would sit down at his desk with a blank piece of paper in front of him. At the end of the day, he would still be staring at the same blank sheet of paper.

Russell’s final resolution to the problem is described in his “Principia Mathematica”, written with Alfred North Whitehead, in which he introduced a “Theory of Types” to get around his paradox. The basic idea was this: sets cannot contain themselves....

http://www.geometer.org/mathcircles/nothing.pdf

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