0
$\begingroup$

a) show that inf(f(x) + g(x)) $\geq$ inf f(x) + inf g(x)

b) Find examples where we obtain strict inequality.

I already proved a), but I have no idea how to find an example for a)..

  • 0
    Try using $D = \{0, 1\}$. – 2017-02-10

1 Answers 1

1

Try to find examples where $f(x)$ takes certain low values, and $g(x)$ also takes certain low values, but they never both do it for the same value of $x$.

  • 0
    I could find $f(x) = (-1) ^n$ and $g(x) = (-1)^{n+1}$, but I used this example for sup f + g $\leq$ sup f + sup g.... hum. need to find another one.. – 2017-02-10
  • 0
    If you mean $f(n)$, then yes, that would work. It works for both. – 2017-02-10