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Indexing Problems

Age 16 to 18 Short
Challenge Level

Consider a very big book, UltraRef, which refers in its index to every book which does not refer to itself in its index.

Does UltraRef refer to itself in its index? Be clear as to your explanation.
Did you know ... ?

Paradoxes are a fascinating feature of more advanced considerations of mathematical logic. For a century mathematicians tried to put mathematics on a totally sure logical foundation before realising that this could never be completely achieved.