Cantor’s original proof of the uncountability of the reals didn’t use a diagonalization argument, it used order + completeness and in fact applies to any comple

Cantor’s original proof of the uncountability of the reals didn’t use a diagonalization argument, it used order + completeness and in fact applies to any complete poset. https://en.wikipedia.org/wiki/Cantor%27s_first_set_theory_article https://en.wikipedia.org/wiki/Cantor%27s_first_set_theory_ar... Likewise his proof that there is no surjection from a set to its power set uses a more general diagonalization argument that doesn’t make any uncomfortable assumptions: https://en.wikipedia.org/wiki/Cantor%27s_theorem https://en.wikipedia.org/wiki/Cantor%27s_theorem