[Verse 1] Zero stands alone, the starting gate No parent made it, no prior state Every number finds its next in line Successor function, step by step divine One follows zero, two follows one Building blocks when math's begun [Chorus] Peano's axioms, foundation stones Zero first, then successors grown No reverse path leads to zero's door Injective steps, each one unique and pure Induction's net catches every case Natural numbers find their rightful place [Verse 2] If successors match, their parents too Must be identical through and through No circular paths can twist and bend Back to zero where all chains must end S of m equals S of n Means m and n are twins again [Chorus] Peano's axioms, foundation stones Zero first, then successors grown No reverse path leads to zero's door Injective steps, each one unique and pure Induction's net catches every case Natural numbers find their rightful place [Bridge] From these five rules, addition grows Recursive patterns, nobody knows Multiplication builds from there No assumptions, crystal clear DNA of counting's art These axioms, the beating heart [Verse 3] If a set holds zero tight And successor closure's right Then every natural must belong Induction makes the argument strong Plus zero equals just itself Plus successor builds more wealth [Chorus] Peano's axioms, foundation stones Zero first, then successors grown No reverse path leads to zero's door Injective steps, each one unique and pure Induction's net catches every case Natural numbers find their rightful place [Outro] From nothing built, the numbers rise No circular disguise Five axioms unlock the gate To arithmetic's estate
← Schröder-Bernstein Theorem (The Matching Miracle) | The Problem →