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The set **R** is *not* countable.

Every infinite sequence `d` of decimal digits represents a real number

0.d_{0}d_{1}d_{2}....

Since the set of all infinite sequences is not countable (and every real
number is represented by a countable set of such sequences), also **R** is
not countable.

*Not all number domains are countable.*

Author: Wolfgang Schreiner

Last Modification: December 7, 1999