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I would like to determine the cardinality of the sets specified bellow. Nevertheless, I don't know how to approach or how to start such a proof. Any help will be appreciated.

If $X$ and $Y$ are well-ordered sets, then determine the cardinality of:

  1. $\{f : f$ is a function from $X$ to $Y\}$
  2. $\{f : f$ is an order-preserving function from $X$ to $Y\}$
  3. $\{f : f$ is a surjective and order-preserving function from $X$ to $Y\}$
  • 0
    Are you allowed to assume the axiom of choice?2011-03-05
  • 0
    @Asaf: Yes, I am.2011-03-05
  • 0
    Oh, any hints yet? I suppose this problem is somewhat complicated.2011-03-05

1 Answers 1