Show that all intervals contained in $[0, 1]$ is a semi-algebra Suppose $J = \{\text{All intervals contained in }[0,1]\}$
I am having trouble showing that the complement of any element of $J$ is equal to a finite disjoint union of elements of $J$.
It seems simple enough - draw a line, cut out one or a few segments, what's left is the disjoint union of elements of $J$. Don't know how to express that mathematically though. 

An element of $J$ is of the form $[a,b], (a,b], [a,b),$ or $(a,b)$ with $0\leq a\leq 1$, $0\leq b\leq 1$ and $a\leq b$.  So, its complement is $[0,a)\cup (b,1]$ or some other appropriate use of ()'s or []'s, which is by definition, a union of two elements of $J$.
