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    #1
    Hey guys,

    I have an Intermediate Analysis problem that needs assistance. I've really been having a hard time with it. This is what the question says:

    "Can it happen that A⊂B (A is a subset of B) and A≠B (A does not equal B), yet sup A=sup B (the supremum of A equals the supremum of B)? If so, give an example. If not, prove why not."

    Honestly, I'm not even sure where to begin with proving this, so any help would be greatly appreciated on my behalf. Thank you in advance to anyone that replies.

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    #2
    Quote Originally Posted by AutGuy98 View Post
    Hey guys,

    I have an Intermediate Analysis problem that needs assistance. I've really been having a hard time with it. This is what the question says:

    "Can it happen that A⊂B (A is a subset of B) and A≠B (A does not equal B), yet sup A=sup B (the supremum of A equals the supremum of B)? If so, give an example. If not, prove why not."

    Honestly, I'm not even sure where to begin with proving this, so any help would be greatly appreciated on my behalf. Thank you in advance to anyone that replies.
    Hi AutGuy98,

    Here is a simple example: take $A=\{1\}$ and $B=\{0,1\}$. You have $\sup A = \sup B = 1$.

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