From f0368f3875c00504c29cbc3fddfcc88419f2d08f Mon Sep 17 00:00:00 2001 From: Barrett Ruth Date: Sun, 22 Jun 2025 14:29:18 -0500 Subject: [PATCH] feat(proofs): correct 993 a --- src/content/posts/algorithms/proofs.mdx | 10 +--------- 1 file changed, 1 insertion(+), 9 deletions(-) diff --git a/src/content/posts/algorithms/proofs.mdx b/src/content/posts/algorithms/proofs.mdx index 39dc3ad..47a964f 100644 --- a/src/content/posts/algorithms/proofs.mdx +++ b/src/content/posts/algorithms/proofs.mdx @@ -20,14 +20,7 @@ Count-Pairs($n$): *Proof.* -For some choice of $a$ there is only one -choice of $b$: $a=n-b\rightarrow b=n-a$. Consider all $a$ from $1,2,\cdots,n$. There are -$n$ such pairs: - -$$(1,n-1),(2,n-2),...,(n,0)$$ - -Excluding the last pair formed when $a=n\rightarrow b=0$, there are $n-1$ possible -ordered pairs. +Suppose $(a,b)\in\mathbb{N}^2$. Because $a=n-b$ and $a\geq1$, it follows that $1\leq b\leq n-1$. Each choice of $b$ yields a unique $a=n-b$, so there are $n-1$ unique solutions. $\blacksquare$ @@ -46,7 +39,6 @@ Mirror-String($s$): The string appears fipped on the y-axis from within the score due to the perspective shifting. Structurally, it is read right-to-left. "p"/"q"/"w" appear as "q"/"p"/"w" when flipped on its y-axis. -when flipped on its y-axis: $\blacksquare$