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anelys
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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.