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## Homework Statement

Let f: [0,1] -> R be a bounded function.

Define S(f,x) = sup { |f(r) - f(s) | : r,s in [0,1] and |r-s| <= x}.

Prove that if x>0, y>0 then:

S(f,x+y) <= S(f,x) + S(f,y).

## The Attempt at a Solution

I have no idea how to proceed, could you please help?