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problem:the_composition_of_permutations_is_a_permutation
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problem:the_composition_of_permutations_is_a_permutation [2013/11/21 10:27] tarafife |
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: | + | Prove theorem [[Theorem: |
| 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 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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problem/the_composition_of_permutations_is_a_permutation.1385047678.txt.gz · Last modified: 2013/11/21 10:27 by tarafife
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