There is nothing missing from the problem. I guess we can assume that it's continuous. It isn't necessarily a decreasing monotone function. Also, yes, c is any point between f(b) and f(a).
Homework Statement
f(a) > c > f(b)
A = { x : b > x > y > a implies f(a) > f(y) }
let u = sup(A)
show that f(u) = c
Homework Equations
I have no idea in particular, save for the definition of the supremum:
\forall x \in A x \le u
if v is an upper bound of A, then u \le v...