Let S be a finite set with n 2 elements and let _ be a partial order on S. For x S, let
Chapter 11, Problem 11(choose chapter or problem)
Let S be a finite set with n 2 elements and let _ be a partial order on S. For x S, let Sx = {y S : x _ y}. Let f : S {1, 2, . . . , n} be a function defined by f(x) = |Sx| for each x S. Prove that f is bijective if and only if (S,_) is a totally ordered set.
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