I considered deleting the post, but this seems more cowardly than just admitting I was wrong. But TIL something!

  • lad@programming.dev
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    10 months ago

    Isn’t cardinality of [0, 1] = cardinality of {0, 1} + cardinality of (0, 1)? One part of the sum is finite thus doesn’t contribute to the result

    • lemmington_steele@lemmy.world
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      10 months ago

      technically yes, but the proof would usually show that this works by constructing the bijection of [0,1] and (0,1) and then you’d say the cardinalities are the same by the Schröder-Berstein theorem, because the proof of the latter is likely not something you want to demonstrate every day