We have $\left|A\right|=k$ and $\left|B\right|=n$. How many surjective functions $\:f\::\:A\to \:B$ exist? Provide a demonstration.
Where $\left|A\right|$ is the cardinal of A.
How to solve this?
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Well, I know that in a surjective functions, for every number in the codomain, we need to have a number in a domain so that f(x) = y, where y is in the codomain and x is in the domain. – MikhaelM Jan 15 '16 at 14:24
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But I don't really know how to go about solving the exercise, and then demonstrate it. I'm guessing I need to find some sort of formula to determine the number of functions that are surjective, based on the sets' cardinals. – MikhaelM Jan 15 '16 at 14:25
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@BrianO: I just upvoted your answer to the earlier question, so you can now vote to close this one. – Brian M. Scott Jan 15 '16 at 23:30
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@BrianM.Scott Thanks much, I will. – BrianO Jan 15 '16 at 23:56