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.
Last edited by Slazenger3; January 28th 2010 at 05:56 PM. Reason: adding something else
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Originally Posted by Slazenger3 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. and . Therefore, . And thus, . That was INTENTIONALLY terse. Make it better.
Originally Posted by Slazenger3 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. Think about functions whose maximum points occur at different values. For example, and . Don't use my example. Find one of your own, but use the basic concept behind it.
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