[Verse 1] Let me tell you 'bout a clever mathematician's game Russell found a puzzle that would never be the same He gathered all the sets that don't hold themselves inside A collection so peculiar, contradictions can't hide [Pre-Chorus] Build a box of every box that doesn't hold its name But when you ask the question, who's really to blame? [Chorus] Russell's Paradox, spinning round and round Does R belong to R? No answer can be found If it's in, then it's out, if it's out, then it's in The circle never stops, where does logic begin? Russell's Paradox, showed us something's wrong Naive set theory couldn't sing this song [Verse 2] Take every set that's not a member of itself Stack them on the mathematical shelf But now we've got a problem with our brand new creation Does our Russell set deserve self-classification? [Pre-Chorus] Check the definition, follow every rule But logic starts to crumble like a broken tool [Chorus] Russell's Paradox, spinning round and round Does R belong to R? No answer can be found If it's in, then it's out, if it's out, then it's in The circle never stops, where does logic begin? Russell's Paradox, showed us something's wrong Naive set theory couldn't sing this song [Bridge] Comprehension principle seemed so clean and neat "Any property makes a set complete" But Russell proved that freedom has a price Some collections just can't roll the dice We need axioms with boundaries drawn tight Powerful enough for math, restrictive enough to get it right [Final Chorus] Russell's Paradox, taught us how to see Not every bunch of things can claim to be A proper set with membership so clear Some contradictions we should always fear Russell's Paradox, wisdom from the past Build your foundations right, make them last [Outro] When you're building mathematics from the ground Make sure your logic stays completely sound
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