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Cantor's original proof considers an infinite sequence S of the form ( s < sub > 1 </ sub >, s < sub > 2 </ sub >, s < sub > 3 </ sub >, ...) where each element s < sub > i </ sub > is an infinite sequence of 1s or 0s.
This sequence s < sub > i </ sub > is countable, as to every natural number n we associate one and only one element of the sequence.
We might write such a sequence as a numbered list:
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