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Aug 2, 2012 at 8:08 comment added Noam D. Elkies But the graph can have an infinite sequence of zig-zags/edges approaching $p$ and still be differentiable at $p$...
May 18, 2010 at 12:25 comment added Martin Brandenburg Yes, but then you should formulate this different way of thinking. In many cases, it happens to be one already mentioned by Thurston.
May 18, 2010 at 1:19 comment added Qiaochu Yuan Different definitions lend themselves to different ways of thinking, so this isn't so bad, I think.
May 18, 2010 at 1:13 comment added KConrad My answer was a way of thinking about the derivative: anything which is additive with a product rule can have all the intuitions and expectations of the derivative applied to it (maybe with some surprises in characteristic p).
May 18, 2010 at 0:51 history answered Martin Brandenburg CC BY-SA 2.5