Uncountably many.

The cardinality of the set of all binary sequences is the same as the cardinality of the continuum (or, if you prefer, the interval (0,1) ). This is more than the number of natural, or counting numbers (which is the same as the number of rational numbers, i.e. the set of numbers of the form a/b where a and b are both integers and b is nonzero).

Posted By: Old Man, Oct 6, 17:07:16