[Verse 1] Two functions walking different ways One from A to B displays Another from B back to A Each injection finds its place Neither surjective, incomplete But something magical we'll meet [Chorus] When arrows flow both directions We can weave perfect connections Schröder-Bernstein shows the way Matching miracle at play If each side fits the other's frame Then both collections are the same [Verse 2] Follow chains that bounce around Elements seeking to be found Some will cycle, some will end Watch the patterns twist and bend Build our bijection piece by piece Let the interweaving increase [Chorus] When arrows flow both directions We can weave perfect connections Schröder-Bernstein shows the way Matching miracle at play If each side fits the other's frame Then both collections are the same [Bridge] Take the chains that start in A minus f-inverse of B Keep original injection's destiny For remaining elements switch Use the backward-pointing switch Partial matchings now complete Perfect pairing, theorem sweet [Chorus] When arrows flow both directions We can weave perfect connections Schröder-Bernstein shows the way Matching miracle at play If each side fits the other's frame Then both collections are the same [Outro] Two injections guarantee Equal cardinality The matching miracle rings true Bijection waiting there for you
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