# Math Help - Supreme of a set

1. ## Supreme of a set

I know it is not necessary for the supreme of a set be an element of the set.
Can someone please justify this by giving suitable examples?

2. ## Re: Supreme of a set

Originally Posted by Kristen111111111111111111
I know it is not necessary for the supreme of a set be an element of the set.
Can someone please justify this by giving suitable examples?
Suppose that $S = \left\{ {1 - {n^{ - 1}}:n \in {Z^ + }} \right\}$.

Now surely $\sup(S)=1$. BUT tell us if $1\in S~?$

3. ## Re: Supreme of a set

Yeah that's superb! Thanks a lot

4. ## Re: Supreme of a set

Similarly: the set of all real number less than one. 1 is the supremum but 1 is not in the set.