"You can define the barber as 'one who shaves all those, and those
only, who do not shave themselves.' The question is, does the barber
shave himself? In this form the contradiction is not very difficult
to solve. — Bertrand Russell, The Philosophy of Logical Atomism."
The confusions, intricacies, and complexities of
infinity can be realized in Russell's paradox. What is Russell's
paradox? The following quote explains it.
"Russell's Paradox is the most famous of the logical or
set-theoretical paradoxes. Also known as the Russell-Zermelo
paradox, the paradox arises within naïve set theory by considering
the set of all sets that are not members of themselves. Such a set
appears to be a member of itself if and only if it is not a member
of itself. Hence the paradox.
A simpler way to understand this is if sets can contain themselves, then the Set of all Sets whether finite or infinite, must be able to contain itself, because it is itself a set; however, when the Set of all Sets, shares the property of the sets that do not contain themselves, then the Set of all Sets must contain itself, but it cannot contain itself. And the paradox is recognized. |

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