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Nice comment. A succinct explanation of the difference between negation and contradiction can also be found in this r/math comment: https://reddit.com/r/math/co

Nice comment. A succinct explanation of the difference between negation and contradiction can also be found in this r/math comment: https://reddit.com/r/math/comments/cu9gsk/_/exse1ps/?context=1 https://reddit.com/r/math/comments/cu9gsk/_/exse1ps/?context... The terminology gets abused a lot, even by professors. It's actually hard to find theorems which really require proof by contradiction.

Smaug123 6y ago
Well, if your logical system defines "not P" as "assuming P, you can derive falsity", then "uncountable" precisely means "if you assume it is countable then you can derive falsity". That's exactly what the proof did. If you particularly care then you can just replace the final word "contradiction" with "QED"; it doesn't change the structure or content of the proof.