I think that you need help with the idea of boundary points.
The point is a boundary point of if and only if .
In other words, in every of contains a point of and a point not in .
Using the definition of supremum, the proof is simple.
Let S be a bounded set that is not empty.
Prove that sup(S) is a boundary point of S
can someone help me complete this proof? i've been trying for a long time and i can't come up with anything other than
If S is a (not empty) set of real numbers and S has an upper bound y,
then there is a least upper bound of the set S.
That least upper bound is also called the supremum of S
please help, i really need it
hmm. see i'm not very good with this. i'm just starting off, and i'm having a hard time with the writing of proofs. it's hard. thanks you though. the definition of a supremum is the LUB on a function over its domain right?kj