[Verse 1] The rationals spread across the line like scattered stones But square root two just can't be found, it's missing from our home There's something lurking in between, a phantom in the gaps Dedekind saw the emptiness and drew his mental maps [Chorus] Cut the line in two parts clean Lower left and upper right Every rational finds its scene But the gaps reveal new sight Cuts ARE numbers, pure and bright Structure makes the real complete [Verse 2] Take every rational you know, divide them at a point Some go left, some venture right, no middle to anoint If you cut right at one-third, that rational you'll find But cut where root-two ought to live, no max or min defined [Chorus] Cut the line in two parts clean Lower left and upper right Every rational finds its scene But the gaps reveal new sight Cuts ARE numbers, pure and bright Structure makes the real complete [Bridge] No maximum below, no minimum above The gap itself becomes the thing we're dreaming of Not substance but relation, not matter but the role The partition IS the number, structure feeds the soul [Verse 3] You can add these cuts together, multiply them too Order them from small to large like numbers always do If it acts just like a number, then a number it shall be Construction beats discovery, we forge reality [Chorus] Cut the line in two parts clean Lower left and upper right Every rational finds its scene But the gaps reveal new sight Cuts ARE numbers, pure and bright Structure makes the real complete [Outro] From quotient rings to Cauchy chains This pattern shows the way Define by role, not by remains Mathematics builds today
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