  We study several variants of a combinatorial game which is based on Cantor's
diagonal argument.
  The game is between two players called Kronecker and Cantor. The names of the
players are motivated by the known fact that Leopold Kronecker did not
appreciate Georg Cantor's arguments about the infinite, and even referred to
him as a "scientific charlatan". In the game Kronecker maintains a list of m
binary vectors, each of length n, and Cantor's goal is to produce a new binary
vector which is different from each of Kronecker's vectors, or prove that no
such vector exists. Cantor does not see Kronecker's vectors but he is allowed
to ask queries of the form"What is bit number j of vector number i?" What is
the minimal number of queries with which Cantor can achieve his goal? How much
better can Cantor do if he is allowed to pick his queries \emph{adaptively},
based on Kronecker's previous replies? The case when m=n is solved by
diagonalization using n (non-adaptive) queries. We study this game more
generally, and prove an optimal bound in the adaptive case and nearly tight
upper and lower bounds in the non-adaptive case.
