This is a proof by contradiction: it shows that any bounded algorithm doesn't have equally probable outputs, i.e., that it is necessarily biased, contradicting our assumption that it is unbiased. Therefore, an unbiased, bounded algorithm cannot exist (for n > 2): any algorithm is necessarily either biased or unbounded.
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This is a proof by contradiction: it shows that any bounded algorithm doesn't have equally probable outputs, i.e., that it is necessarily biased, contradicting our assumption that it is unbiased. Therefore, an unbiased, bounded algorithm cannot exist (for n > 2): any algorithm is necessarily either biased or unbounded.