Propp himself (the author) wrote a paper in 2012 called Real Analysis In Reverse, which he links to in the post but doesn't really call attention to. It's a lov

Propp himself (the author) wrote a paper in 2012 called Real Analysis In Reverse, which he links to in the post but doesn't really call attention to. It's a lovely paper, and it talks about precisely what properties of the reals are enough to tell you that you really are dealing with the reals - like his example of the Constant Value Theorem from the post. https://arxiv.org/abs/1204.4483 https://arxiv.org/abs/1204.4483