[Verse 1] In the realm where mathematics grows precise We need rules to build our paradise Not defining what a set could be Just declaring what exists, you see Extensionality starts the show Two sets equal when their contents flow Exactly matching, element by element No hidden differences, no argument [Chorus] ZFC axioms, ten foundations strong Empty set and pairing, singing set theory's song Union, power, infinite chains Separation blocks the paradox pains Replacement builds and Foundation guards Choice selects from scattered shards These are the rules that make sets real ZFC axioms, mathematics' steel [Verse 2] Empty set exists with nothing inside Pairing takes two sets for a ride Makes a new one holding both as treasure Union gathers collections beyond measure Power set creates all subsets dancing Infinity gives us numbers advancing Zero, successor, successor again Natural numbers in an endless chain [Chorus] ZFC axioms, ten foundations strong Empty set and pairing, singing set theory's song Union, power, infinite chains Separation blocks the paradox pains Replacement builds and Foundation guards Choice selects from scattered shards These are the rules that make sets real ZFC axioms, mathematics' steel [Bridge] Separation says you cannot form Sets from nothing but the storm Start with something, filter down Russell's paradox won't come around Replacement maps with function's grace Foundation keeps sets in their place No descending membership falls Choice picks elements through it all [Chorus] ZFC axioms, ten foundations strong Empty set and pairing, singing set theory's song Union, power, infinite chains Separation blocks the paradox pains Replacement builds and Foundation guards Choice selects from scattered shards These are the rules that make sets real ZFC axioms, mathematics' steel [Outro] From these ten axioms, mathematics blooms Set theory fills up all the rooms What exists and what we can create ZFC seals mathematics' fate
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