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Added: 24a25,26
That's not a one-to-one mapping. Representations of numbers in the CantorSet are unique, but binary representations aren't: 0.022222... != 0.20000... but 0.01111... = 0.10000... Of course it's still a SurJection?, so proves the objects are the same cardinality. Any ideas on how an actual BiJection could be made, though? I'm curious.