Practice question · Multiple choice
Is there a set of all sets? Russell asked instead about the set of all sets that do not contain themselves. Why is that question fatal?
Hints
- Call the set R. Ask whether R is a member of R, and follow both branches.
- The description is perfectly precise. That is what makes it dangerous.
Show the answer
A. Because it contains itself exactly if it does not
Why
Both answers refute themselves, and the description was flawless, so the fault is in the assumption that any description defines a set. Modern axioms build sets from existing ones instead, which is the whole reason set theory looks so bureaucratic: it is arranged to make this sentence unwriteable.
Practise Sets and Set-Builder Notation
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