Find the number of all onto functions from the set A = {1, 2, 3, ..., n} to itself.

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Solution

We know that every onto function from A to itself is one-one.
So, the number of one-one functions = number of bijections = n!

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Find the number of all onto functions from the set A = {1, 2, 3, ..., n} to itself.

We know that every onto function from A to itself is one-one. So, the number of one-one functions = number of bijections = n!

We know that every onto function from A to itself is one-one.
So, the number of one-one functions = number of bijections = n!