Russell's paradox

What if you find a set that defies its own rules?

Imagine you're sorting your collection of unique pens. You decide to create a special pen holder for pens that don't belong to themselves. But then you wonder, does this pen holder belong to itself?

You're trying to sort pens into a holder that only holds pens not belonging to themselves. But then you hit a wall: if you decide this holder belongs to itself, it shouldn't, and if it shouldn't, it should. This contradiction is Russell's paradox.

Example

You have a pen that doesn't fit into any other pen holder. You create a holder for pens like this one. But then you ask, does this holder belong to itself?

Remember this

Russell's paradox shows that naive set theory's unrestricted comprehension principle leads to contradictions, challenging its foundation.

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

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