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""The set of all sets that are not members of themselves"

A set can either be a member of itself or not. The set of all mathematical objects is a mathematical object so it's a member of itself. The set of all sets with only three members has an infinite number of members so it's not a member of itself.

There must be a set of all sets that are members of themselves and therefore a set of all sets that are not members of themselves. Is that set a member of itself?

This is a problem which has no solution. I leads us to Godel's incompleteness theorem (that no mathematical system can be both consistent and complete) which is an even bigger problem.

Mark Kelly


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