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Prove that, for all $n \geq 1$, $|\set{s \in \bit^n : K(s) < n}| \leq 2^n-1$, i. e.\ there are at most $2^n-1$ binary strings of length $n$ that have Kolmogorov complexity strictly less than $n$.

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Prove that, for all $n \geq 1$, $|\set{s \in \bit^n : K(s) < n}| \leq 2^n-1$, i. e.\ there are at...
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