http://www.uea.ac.uk/~j108/diagonalisation.htm
Interesting Russels argument
There is a greatest of all infinite numbers, which is the number of all things altogether, of every sort and kind. It is obvious that there cannot be a greater number than this, because if everything has been taken, there is nothing left to add. Cantor has a proof that there is no greatest number… But in this point, the master has been guilty of a very subtle fallacy, which I hope to explain in some future work.
Russell, ‘Mathematics and Metaphysicians’, 1901
Within a system of thought we always feel like this: surely this is everything... but that is because the system limits our view... it is the escaping the system (of Natural numbers here) the aufhebung in German which Russel over looks the possibility of.
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