What if sets could contain themselves, and that led to a logical conundrum?
Set theory
What if sets could contain themselves, and that led to a logical conundrum?
Imagine you have a collection of boxes, and some boxes say they don't contain themselves. But then you wonder if there's a box that says it contains all boxes that don't contain themselves. How do you sort this out?
You can't have a box that includes itself and doesn't include itself at the same time. This idea led to Russell's paradox, showing a flaw in naive set theory.
Example
You have a box labeled "Boxes that don't contain themselves." Now, you ask if this box contains itself. If it does, it shouldn't, and if it doesn't, then it should because it's a box that doesn't contain itself.
Remember this
Russell's paradox shows that naive set theory can't handle self-referential sets without causing contradictions.
Text adapted from Wikipedia, licensed under CC BY-SA 4.0.
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