TITLE: What is the Shortest possible formula to find the intersection between a set of two ranges of number
QUESTION [7 upvotes]: How to find the intersection between a set of two ranges of number.
let me explain the question with an example,
{2,3} {3,8} would result to 0
{2,5} {3,8} would result to 2
{3,6} {3,8} would result to 3
{4,5} {3,8} would result to 1
{4,5} {3,8} would result to 1
{8,9} {3,8} would result to 0

Note:This could be easily done with series of if in a computer application, I am hungry for a mathematical solution!

REPLY [11 votes]: If I understood you correctly, you have $\{x,x+1,\ldots,x+n\}$ and $\{y,y+1,\ldots,y+k\}$ and granted $x,y$ are integers you want to find out the number of elements in the intersections (i.e. how many numbers appear in both sets).
Well, take: $$\max\{0,\min\{y+k,x+n\}-\max\{x,y\}\}$$ and that should be it.