Give an example of an open set in R under the usual topology that is not expressible as the union of a finite number of intervals Give an example of an open set in R under the usual topology that is not expressible as the union of a finite number of intervals.
My introduction to proofs class tutorial this week is discussing closed sets... I have feeling giving this example will lead to closed sets? 

$$A:= \bigcup_{n \in \mathbb{N}} (n,n+1)$$ isn't because it's an unbounded open set. Any finite union of open intervals equal to it would therefore have to contain an interval of the form $(a, \infty)$, which would contain natural numbers. $A$ doesn't.
