Let I=(a,b) and J=(c,d) with I and J having a nonempty intersection. Find a formula for the intersection of I and J and prove it. When a<c I have found that the intersection is [c,b]. Now I need to prove that it is. The way I intend to prove it is by showing that [c,b] and the intersection of I and J are both subsets of each other. I've done one, [c,b] being a subset of I intersect J. I intersect J being a subset of [c,b] is a bit trickier. I've broken it down to: let x be an element of I intersect J then x is an element of I and x is an element of J. Then: a<=x<=b and c<=x<=d. Now this is where I'm stumped.