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Feb 17, 2022 at 22:02 comment added Tom Leinster Thanks. I think I'd count that as an example where a significant new idea was needed to pass from the proof using choice to the proof without. As I understand the history, Cantor first proved the theorem using the same proof as you, and only later did Bernstein find a choice-free proof, which was entirely different. (Schröder's only contribution was a wrong proof which he later retracted, but somehow his name stuck -- at least in English. The French, more accurately, call it the Cantor-Bernstein theorem.)
Feb 17, 2022 at 21:47 history made wiki Post Made Community Wiki by Stefan Kohl
Feb 17, 2022 at 21:22 history answered Michael Hardy CC BY-SA 4.0