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@@ -313,7 +313,7 @@ which means it's sufficient to compare $𝐚$ and $𝐛$ directly.
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With a PoW mining system, we are guaranteed to always have that the block hash
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$h(b) ≤ T(b)$. Since the block hashes $( h(b₁), …, h(bₘ) )$ for a sequence
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-$( b₁, …, bₘ )$ have the property that $∑ h(bᵢ) ≤ T(bᵢ)$, as well as being
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+$( b₁, …, bₘ )$ have the property that $∑ h(bᵢ) ≤ ∑ T(bᵢ)$, as well as being
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sufficiently random, we can use them to define our work function.
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Because $W$ is required to be additive, we define a block work function
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@@ -349,8 +349,6 @@ construct two distinct sequences $𝐚 = (a₁, …, aₘ)$ and $𝐛 = (b₁,
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such that $H(a₁) + ⋯ + H(aₘ) = H(b₁) + ⋯ + H(bₙ)$.*
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By property (2), we cannot find a $H(x) = 0$.
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-This means we cannot construct an $x$ such that $H(x) + H(a) = H(b)$ for
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-any $a, b ∈ ℕ$.
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+Again by (2), we cannot construct an $x$ such that $H(x) + H(a) = H(b)$ for
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+any $a, b ∈ ℕ$. Recursive application of (2) leads us to the stated theorem.
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-Let $y = (H(b₁) + ⋯ + H(bₙ)) - (H(a₂) + ⋯ + H(aₘ))$, then we cannot find
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-any $H(x) = y$ by property (2) for $H$.
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zero