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Let $x=(x_1, x_2, \dots x_n) \in \{0,1\}^n$ By $H(x)$ we mean the number of 1's in $(x_1, x_2, \dots x_n)$. Prove that $H(x) = \frac{1}{2} (n-\Sigma^n_{i=1} (-1)^{x_i})$.
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What do we mean by 'x'? Is it the set of n, n-bit binary numbers? How do we build set x? How do we consider the elements in set x?

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