From 98c841f72e933abacf22a5bccf84a38f18569aef Mon Sep 17 00:00:00 2001 From: Mark Date: Mon, 1 Apr 2024 07:21:08 -0700 Subject: [PATCH] Minor edits --- Advanced/Error-Correcting Codes/parts/00 detection.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/Advanced/Error-Correcting Codes/parts/00 detection.tex b/Advanced/Error-Correcting Codes/parts/00 detection.tex index e356b83..2cfd4c5 100755 --- a/Advanced/Error-Correcting Codes/parts/00 detection.tex +++ b/Advanced/Error-Correcting Codes/parts/00 detection.tex @@ -8,7 +8,7 @@ Say we have a sequence of nine digits, forming a partial ISBN-10: $n_1 n_2 ... n The final digit, $n_{10}$, is chosen from $\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ so that: $$ - \sum_{i = 1}^{10} (11 - i)n_i + \sum_{i = 1}^{10} (11 - i)n_i \equiv 0 \text{ mod } 11 $$ If $n_{10}$ is equal to 10, it is written as \texttt{X}. @@ -31,7 +31,7 @@ Only one of the following ISBNs is valid. Which one is it? \problem{} Take a valid ISBN-10 and change one digit. Is it possible that you get another valid ISBN-10? \par -Provide an example or a proof. +Provide a proof. \begin{solution} Let $S$ be the sum $10n_1 + 9n_2 + ... + 2n_9 + n_{10}$, before any digits are changed.