1.) Prove that if f and g are bounded above on a nonempty set S, then sup(f+g) is less than or equal to sup f + sup g.
2.) Give an example of two bounded functions f and g on the interval [0,1] such that sup(f+g) < sup f + sup g.
1.) Prove that if f and g are bounded above on a nonempty set S, then sup(f+g) is less than or equal to sup f + sup g.
2.) Give an example of two bounded functions f and g on the interval [0,1] such that sup(f+g) < sup f + sup g.