[Verse 1] Two sets standing face to face, measuring their size Alice maps to Bob completely, each element finds its place One-to-one but not exhaustive, arrows pointing right Bob sends functions back to Alice, mirroring the sight [Chorus] If A fits into B, and B fits into A Then they're exactly equal, that's what mathematicians say Injection both directions means bijection lives between Cantor-Bernstein-Schröder, the theorem reigns supreme No need to build the bridge direct, just prove the paths exist Two one-way streets become a highway, paradox dismissed [Verse 2] Infinite hotels cause confusion, guests in endless rows Hilbert's puzzles seem impossible when intuition grows But this theorem cuts through chaos, brings order to the strange Equal cardinalities emerge from injection's range [Chorus] If A fits into B, and B fits into A Then they're exactly equal, that's what mathematicians say Injection both directions means bijection lives between Cantor-Bernstein-Schröder, the theorem reigns supreme No need to build the bridge direct, just prove the paths exist Two one-way streets become a highway, paradox dismissed [Bridge] Constructive proof eludes us, but existence is enough When mapping seems impossible, this theorem calls the bluff Three names upon the banner, their legacy remains Comparing vast infinities through logical chains [Chorus] If A fits into B, and B fits into A Then they're exactly equal, that's what mathematicians say Injection both directions means bijection lives between Cantor-Bernstein-Schröder, the theorem reigns supreme [Outro] Sets that seemed unequal, now we know they match Bidirectional injections, that's the perfect catch
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