Let be bounded above, then prove that Let since is bounded above, there's supremum, hence then I'm on the right track? How do I finish? I think I'm wrong.
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Here's what you do: First show that . You've pretty much done that already. Now you need to show that . There are a lot of ways to do that. One way is by contradiction: Suppose . Then , which means that there is some number with , a contradiction.
Originally Posted by Connected Let be bounded above, then prove that Let since is bounded above, there's supremum, hence then I'm on the right track? How do I finish? I think I'm wrong. How did you go from a + c <= c + sup A to sup(a + c) <= c + sup A?
Originally Posted by hatsoff Here's what you do: First show that . You've pretty much done that already Just a thing: I determined that can I change for ? The reason I took is because I didn't want to say since is a set and it's supremum is a scalar, so that doesn't make sense.
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