Yes, the number of all into functions from the set {1, 2, 3, .... n} to itself is exactly equal to the number of many-to-one functions for all positive integers n, as both are quantified by the formula n^n - n!
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Monday, July 20, 2026
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find the number of all ONE - ONE functions from the set {1, 2, 3, ..... n} to itself
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It is same as number of all ONTO functions, because if a set of FINITE number of elements is ONTO then it is ONE - ONE too.
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Is the number of all INTO functions from the set {1, 2, 3, ..... n} to itself equal to all number of MANY to ONE fuctions?
Yes, t he number of all into functions from the set {1, 2, 3, .... n} to itself is exactly equal to the number of many-to-one functions ...
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