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## 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:

[tex]\forall x \in A x \le u[/tex]

if [tex]v[/tex] is an upper bound of A, then [tex]u \le v[/tex]

## The Attempt at a Solution

My intuition led me to attempt a proof by contradiction. If you let f(x*) = c, assume that x* < u to arrive at a contradiction. Then assume that x* > u to arrive at a contradiction. Then to conclude that x* must be u. I don't know how to do this, or even if I can/should be done.