From ec3cf3b27fad1cf300b3c30f59159d56fc03f655 Mon Sep 17 00:00:00 2001 From: Mark Date: Fri, 16 Feb 2024 08:33:54 -0800 Subject: [PATCH] Typo --- Advanced/Cryptography/parts/challenge.tex | 11 +++++++---- 1 file changed, 7 insertions(+), 4 deletions(-) diff --git a/Advanced/Cryptography/parts/challenge.tex b/Advanced/Cryptography/parts/challenge.tex index cc0d02a..03d393e 100755 --- a/Advanced/Cryptography/parts/challenge.tex +++ b/Advanced/Cryptography/parts/challenge.tex @@ -27,13 +27,13 @@ This means that we can \say{cancel} operations in groups, much like we do in alg \problem{} Let $G$ be the set of all bijections $A \to A$. \par Let $\circ$ be the usual composition operator. \par -Is $(G, \circ)$ a group? -\vfill +Is $(G, \circ)$ a group? +\vfill \definition{} Note that our definition of a group does \textbf{not} state that $a \ast b = b \ast a$. \par Many interesting groups do not have this property. -Those that do are called \textit{abelian} groups. \par +Those that do are called \textit{abelian} groups. \par \vspace{2mm} @@ -179,5 +179,8 @@ $\gcd(ac + b, a) = \gcd(a, b)$ \par \vfill -[Note on \ref{eua_runtime}] This proof can be used to show that the Euclidean algorithm finishes in logarithmic time, and it is the first practical application of the Fibonacci numbers. If you have finished all challenge problems, finish the proof: show that the Euclidean runs in $O(\log{n})$ +[Note on \ref{eua_runtime}] This proof can be used to show that the Euclidean +algorithm finishes in logarithmic time, and it is the first practical application +of the Fibonacci numbers. If you have finished all challenge problems, +finish the proof: show that the Euclidean algorithm runs in $O(\log{n})$ \pagebreak \ No newline at end of file