[Verse 1] When sets are dancing, side by side How do we know their matching size? Functions hold the secret key Bijections show equality Every element finds its pair Perfect matching, nothing spare One-to-one and onto too That's how cardinality breaks through [Chorus] Same size means bijection's there Arrows pointing everywhere Less than means injection flows But bijection never shows Equal sets have perfect maps Bridge the mathematical gaps Functions tell us who's how big That's the cardinality gig [Verse 2] Injection means we're flowing clean No collisions in between Each input gets its own address But outputs might be loneliness Some targets sitting all alone No arrows calling them their home This tells us A is small or same As B within this mapping game [Chorus] Same size means bijection's there Arrows pointing everywhere Less than means injection flows But bijection never shows Equal sets have perfect maps Bridge the mathematical gaps Functions tell us who's how big That's the cardinality gig [Bridge] Strictly smaller needs a twist Injection yes, bijection missed Can't find that perfect dancing floor Where every guest gets something more Cantor showed us infinite ways Sets can grow through function maze Even numbers, naturals too Bijections make them equal through [Verse 3] Formal symbols paint the scene Vertical bars show what we mean A's size compared to B's domain Through functions we can ascertain Less than equal, just a shot Perfect match or maybe not Equal means the bridge is built Every element finds its guilt [Final Chorus] Same size means bijection's there Arrows pointing everywhere Less than means injection flows But bijection never shows Equal sets have perfect maps Bridge the mathematical gaps Functions tell us who's how big That's the cardinality gig [Outro] Count through functions, not through numbers That's where true mathematics slumbers Bijections are the golden thread Weaving sets from A to Z
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