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problem:the_composition_of_permutations_is_a_permutation [2013/11/21 10:15]
tarafife [External links] 		problem:the_composition_of_permutations_is_a_permutation [2013/11/21 10:30] (current)
tarafife
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 ====== The Composition Of Permutations Is A Permutation ====== ====== The Composition Of Permutations Is A Permutation ======
 ==== Problem ==== ==== Problem ====
-Prove theorem [[Theorem:The Composition Of Permutations Is A Permutation]]).  +Prove theorem [[Theorem:The Composition Of Permutations Is A Permutation]].  
 As some reminders, you may use the following facts that you proved in either Math 301 or Math 340. You may use these facts without proof.   As some reminders, you may use the following facts that you proved in either Math 301 or Math 340. You may use these facts without proof.  
-  - The composition of two injective functions is injective. +  * The composition of two injective functions is injective. 
-  - The composition of two surjective functions is surjective. +  * The composition of two surjective functions is surjective. 
-  - A function is a bijection if it is both injective (1 to 1) and surjective (onto). Hence, the composition of two bijective functions is a bijection.  +  * A function is a bijection if it is both injective (1 to 1) and surjective (onto). Hence, the composition of two bijective functions is a bijection.  
-  - You might find induction helps you get from a composition of two bijective functions is bijective to the composition of $n$ bijective functions is bijective.  +  * You might find induction helps you get from a composition of two bijective functions is bijective to the composition of $n$ bijective functions is bijective.  
  
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 Prove theorem [[Theorem:The Composition Of Permutations Is A Permutation]]).   Prove theorem [[Theorem:The Composition Of Permutations Is A Permutation]]).  
 As some reminders, you may use the following facts that you proved in either Math 301 or Math 340. You may use these facts without proof.   As some reminders, you may use the following facts that you proved in either Math 301 or Math 340. You may use these facts without proof.  
-\begin{enumerate}+\begin{itemize}
 \item The composition of two injective functions is injective. \item The composition of two injective functions is injective.
 \item The composition of two surjective functions is surjective. \item The composition of two surjective functions is surjective.
 \item A function is a bijection if it is both injective (1 to 1) and surjective (onto). Hence, the composition of two bijective functions is a bijection.  \item A function is a bijection if it is both injective (1 to 1) and surjective (onto). Hence, the composition of two bijective functions is a bijection. 
-\end{enumerate} +\item You might find induction helps you get from a composition of two bijective functions is bijective to the composition of $n$ bijective functions is bijective.  
-  - You might find induction helps you get from a composition of two bijective functions is bijective to the composition of $n$ bijective functions is bijective.  +\\end{itemize} 
-\end{problem}+end{problem}
 </file> </file>
  
problem/the_composition_of_permutations_is_a_permutation.1385046919.txt.gz · Last modified: 2013/11/21 10:15 by tarafife

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