How many surjective functions are there when mapping a n-set to a k-set?

Question

Is there some kind of relation, like maybe a recurrence relation or something?

Answer 1

My favorite part of taking calculus has been forgetting it.

I still use algebra fairly regularly in my adult life, but I have never found a practical application for calculus in any job or hobby I've had.

Answer 2

It's going to be kCn; you're taking a set of size n and choosing positions for them out of a set of size k. (That's n!/(k!*(n-k)!), analytically.)

If you're trying to figure out the analytics of that combinatoric process for the first time, you can think of it as taking the elements from set n one by one, assigning them a mapping in set k, and then going to the next one until you run out of elements in set n. In this process, there are always k - i + 1 mapping possibilities for the element from set n where i is the iteration index of the process. Solve the resulting sigma expression and you come up with the normal kCn expression.

Answer 3

Wrong section much?

Answer 4

n-set to the whatnow ?