[Verse 1] Between the naturals and the reals There lies a question math reveals Are there sets that fit between These infinities we've always seen Aleph-null counts the integers But real numbers go much further [Chorus] The Continuum Hypothesis stands alone Can't be proved, can't be overthrown No middle ground between the two Aleph-one equals reals, is it true? Independent from our axioms This mystery will keep on living [Verse 2] Gödel showed in nineteen-forty That assuming it's not faulty ZFC remains consistent Cohen proved the oppositeistent Nineteen sixty-three he found Negation keeps the system sound [Chorus] The Continuum Hypothesis stands alone Can't be proved, can't be overthrown No middle ground between the two Aleph-one equals reals, is it true? Independent from our axioms This mystery will keep on living [Bridge] Countable infinity Uncountable reality Where does the gap lie? Mathematics asks us why Some truths we cannot reach Beyond what axioms teach [Verse 3] Cardinals climb the ladder high Aleph-null is where we start to fly But what comes next in order? Is there anything that borders The power of the real line? This question transcends space and time [Chorus] The Continuum Hypothesis stands alone Can't be proved, can't be overthrown No middle ground between the two Aleph-one equals reals, is it true? Independent from our axioms This mystery will keep on living [Outro] In the realm of set theory Some questions stay in mystery Neither true nor false we find The limits of the human mind
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