Here is the question:

Given $\displaystyle X=\{x_j\}_{j\in J}\in\Re$ (X is the set of all Dedekind cuts, sorry if that's obvious), show that the least upper bound of $\displaystyle X=\bigcup_{j\in J}x_j$

Is the least upper bound supposed to be a Dedekind cut itself, so of the form $\displaystyle x_i$, or is it an element $\displaystyle m\in\Re$? I think I understand how to do this otherwise, but any guidance would be helpful. Thank you!