# Proof of the Equality of Supremums (Or Something Like That Anyway :) )

#### AutGuy98

##### New member
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.

#### castor28

##### Well-known member
MHB Math Scholar
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 $\sup A = \sup B = 1$.