this post was submitted on 06 Jan 2024
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EDIT: I THINK I STAND CORRECTED (lemmy.zip)
submitted 10 months ago* (last edited 10 months ago) by [email protected] to c/[email protected]
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I considered deleting the post, but this seems more cowardly than just admitting I was wrong. But TIL something!

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[–] sukhmel 1 points 10 months ago (1 children)

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

[–] [email protected] 2 points 10 months ago* (last edited 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