Real Analysis 187

Credits

I was put on to the principle of continuous induction by Pete Clark, whose excellent

manuscript, Clark (2019), includes an account of this principle and many interesting ap-

plications, as well as a history of the idea, which evidently goes back at least to Aleksandr

Khinchin in 1922 and the earlier instance with Chao (1919) that I mentioned. Chao’s ver-

sion probably should not be considered a true version of continuous induction, however,

because of his uniform-increase requirement and the lack of equivalence with the com-

pleteness principle.