Has anyone read Stillwell's "Reverse Mathematics" and is willing to explain some of the intro chapter to me? The section on page 3 about the parallel axiom looks entirely wrong to me and I'm sure this is my misunderstanding rather than an error but I'm baffled and don't see how.
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Relevant page. As far as I can tell: 1. The version of the parallel axiom stated is also true in spherical geometry (because all lines meet on each side) 2. The axiom is not used anywhere in the thing that is claimed to follow from itpic.twitter.com/1hUrTfMkEd
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This book has come well recommended and my mathematics is rusty so I'm sure this is my error and not the author's, I'm just perplexed.
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Replying to @DRMacIver
i can take a look at this after i get some sleep in ~9 hours if you still need it
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Replying to @QiaochuYuan
Thanks! I'll add to the thread if my confusion is resolved by then
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you're right on both counts, i think the statement can be fixed if it's changed to "if and only if"?
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