[Verse 1] When the problem seems too big to prove And one approach just will not do Break it down into separate parts That's where proof by cases starts Cover every possibility Leave no gap for doubt to see Finite pieces, check them all Watch the whole solution fall [Chorus] Split it up, break it down Every case must be found Prove each piece, one by one Till the whole proof is done Exhaustion is the key Cover all you can see Cases complete, no stone unturned That's how mathematics is learned [Verse 2] Take absolute value times absolute value X and Y both real and true Four cases emerge from the divide Both positive, we can't hide Both negative, flip the signs One of each, the proof aligns Zero present, easy street Make each case proof complete [Chorus] Split it up, break it down Every case must be found Prove each piece, one by one Till the whole proof is done Exhaustion is the key Cover all you can see Cases complete, no stone unturned That's how mathematics is learned [Bridge] Don't miss a case, that's the trap Leave a hole, proof will snap Natural partitions guide the way Finite choices save the day When no single path will do Cases method sees you through [Verse 3] Check your work, did you cover all Every branch, both big and small If a case slips through the cracks Your whole argument attacks But when every path is clear Victory is drawing near Exhaustive proof stands tall and true Cases method carried you [Chorus] Split it up, break it down Every case must be found Prove each piece, one by one Till the whole proof is done Exhaustion is the key Cover all you can see Cases complete, no stone unturned That's how mathematics is learned [Outro] When the problem's complex and wide Let the cases be your guide Split and conquer, prove each part That's the proof by cases art
← Mathematical Induction | Existence and Uniqueness Proofs →