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'Weekly Challenge 15: Indexing Problems' printed from http://nrich.maths.org/
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.