[Verse 1] When you need to prove infinity's claim Start with one domino in the chain Base case first, check it's true Then assume what P of k can do [Chorus] Base and step, that's the trick Mathematical induction's quick Prove it works for number one Then show k leads to k plus one Dominoes will tumble down Infinite truth is what we've found [Verse 2] Take the sum from one to n Equals n times n plus one, then divide by two First check one equals one, it's right Now assume our formula's tight [Chorus] Base and step, that's the trick Mathematical induction's quick Prove it works for number one Then show k leads to k plus one Dominoes will tumble down Infinite truth is what we've found [Bridge] Add k plus one to both sides clean Factor out what can be seen K plus one times k plus two over two The pattern holds, the proof pulls through [Verse 3] Strong induction takes them all Every case before the call Well-ordering finds the least Contradiction ends the feast [Chorus] Base and step, that's the trick Mathematical induction's quick Prove it works for number one Then show k leads to k plus one Dominoes will tumble down Infinite truth is what we've found [Outro] Finite minds prove endless claims Through induction's clever games Set the chain and flick the start Mathematics' beating heart
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