Mathematics
The Inclusion-Exclusion Principle for Counting with Overlapping Sets
Quick fact
The inclusion-exclusion principle, known since ancient times, allows exact counting of overlapping sets by alternating addition and subtraction of intersections, and it even extends to an infinite number of sets when formalized with measure theory.
Why this is interesting
You need to count everyone in a group who likes either pizza or sushi, but many like both. Simply adding the two counts would double-count those with both. How do you get the exact total?