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The set of all infinite sequences over {0, 1} is not countable.

If it were, we had an f: N ->bijective (N -> {0,1}). Let s: N -> {0, 1}

s(i) := f(i)i
where d := 1-d. Then s differs from f(i) in the i-th digit (for every i in N), thus s is not contained in f.
f(0) =
f(1) =
f(2) =
f(3) =
s :=
... ... ... ... ...

Author: Wolfgang Schreiner
Last Modification: December 7, 1999

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