
MHB Apprentice
#1
September 11th, 2019,
21:50
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 AâŠ‚B (A is a subset of B) and Aâ‰ 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.

September 11th, 2019 21:50
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MHB Craftsman
#2
September 12th, 2019,
04:33
Originally Posted by
AutGuy98
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 AâŠ‚B (A is a subset of B) and Aâ‰ 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 $\sup A = \sup B = 1$.