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A Close Match
Can you massage the parameters of these curves to make them match as closely as possible?
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.
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.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.