Mathematics
The Epsilon-Delta Definition of a Limit
Quick fact
The epsilon-delta definition of a limit, first rigorously formulated by Karl Weierstrass in the 19th century, eliminated centuries of vague reasoning in calculus and made it a truly logical discipline.
Why this is interesting
You can get as close as you want to a target, but how close is close enough? The epsilon-delta definition turns that fuzzy idea into a mathematical precision game.