Mathematics
Principle of Mathematical Induction
Quick fact
Mathematical induction works by proving two things: the base case (often n=0 or n=1) and the inductive step (if the statement holds for n, it holds for n+1). This is enough to prove the statement for all natural numbers, even though there are infinitely many.
Why this is interesting
Imagine lining up dominoes so that knocking the first one topples the second, and each topples the next—then all fall. But how do you know they all fall without actually watching an infinite line? Mathematical induction gives a proof that they do, using just two steps.