Mathematical Induction

You want to prove something holds for 1, 2, 3, 4, … all the way to infinity. Checking each one would take forever. Induction is the shortcut: picture an endless line of dominoes. If you can (1) tip the first one over, and (2) guarantee that any falling domino knocks over the next, then ALL of them fall — no matter how many there are. That's a complete proof for infinitely many cases from just two checks.