[Verse 1] In the halls where logic dwells, there's a statement strange and bold Says you can pick from every box without a method to behold No construction, no direction, just the faith that choice exists When infinity's collections leave your fingers in the mist [Chorus] Axiom of Choice, the phantom selector Zorn's Lemma whispers, Well-Ordering protector Every set can dance in perfect parade But the ghosts it conjures make mathematicians afraid Choice without voice, power without proof Beautiful theorems beneath controversy's roof [Verse 2] Vector spaces find their backbone, every basis guaranteed Products multiply like magic, topology's greatest need Tychonoff and Hahn-Banach owe their lives to this decree But lurking in the shadows waits a terrible mystery [Chorus] Axiom of Choice, the phantom selector Zorn's Lemma whispers, Well-Ordering protector Every set can dance in perfect parade But the ghosts it conjures make mathematicians afraid Choice without voice, power without proof Beautiful theorems beneath controversy's roof [Bridge] Vitali sets emerge unmeasured, length becomes a phantom word Banach-Tarski splits the apple, one ball becomes a pair absurd Gödel proved we cannot banish, Cohen showed we cannot prove Independence reigns eternal in this mathematical groove [Verse 3] So we stand before the crossroads, useful power in our palm Accept the non-constructive blessing or abandon theorem's calm Philosophy dressed as axiom, beauty wrapped in doubt's embrace The choice to make about the Choice that haunts our reasoning space [Outro] In ZF we trust the basics, but AC remains apart A question mark in formal robes that challenges the heart
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