5 ms·

It would be nice to be rewarded for the effort. They should reveal who wrote which proof after the user has answered all questions.

• alainbryden 14y ago
  Yep. When I got not result after carefully considering my first answer, I quit.
  • pohl 14y ago
    Same here. Which one did you pick? I chose (a) because it began so nicely by stating the goal clearly, something that humans often omit.
    • qb45 14y ago
      I think (a) may be the undergrad student - still young and idealistic :) Then (b) could be the PhD student who talked to enough people to be aware that you never know what others consider a ball. Finally, (c) goes to computer because it's the longest one and it's full of Greek letters. I've known a PhD who believed only in proofs starting with "For arbitrary ε > 0, take δ = ...", but even he wasn't as boring as (c).
    • shmageggy 14y ago
      It's almost certainly (c), and the rest of the ones that end with "and we're done". The first one is probably not (a) because it has a pronoun ("it's"), which would be a pain to program into a natural language process for this limited purpose.
    • AimHere 14y ago
      I think it's not (a) There's a line in that proof saying r=min{a,b}; normally I take that to mean r is the minimum of a and b (which makes the proof wrong, since not all metric spaces have obvious orderings on their elements. Spaces like the complex plane or the 2d plane, with an appropriate metric, for instance. I suppose it could mean r is the point in {a,b} such that the ball B_a(x) or B_b(x) has the smallest radius - but that looks more like a human making a notational mistake, particularly given that both 1b) and 1c) use min(,) in a way that seems correct to me (since they're using min on the values of the metric, not the elements of the metric space. AFAICT, either the prover made a mistake in logic or a mistake with notation - which I reckon makes him or her human. Then again, it's been years and years since I thought about this stuff, and I was prone to making mistakes all the time when I did, so everything above might well be wrong. My neurons are getting all fuzzy these days.
      • sn6uv 14y ago
        a and b are real numbers, namely the radius of two balls. They forgot to define B_a, but typically B_a(x) := {y in X : d(x, y) < a} where (X,d) is the metric space. I agree with you though, I don't think it's option (a)
      • mturmon 14y ago
        "...which makes the proof wrong, since not all metric spaces have obvious orderings on their elements..." Your reasoning here is wrong. The "a" and "b" come from the range space of the metric, which by definition associates a pair of points in the metric space (unnamed, but call it X) with a nonnegative real number. In short, "a" and "b" are in R, not in the original metric space X, so it's legal to take the lesser of a and b.
        • AimHere 14y ago
          Oops yes. I see that now. I told you I was rusty!
    • mturmon 14y ago
      I chose (a) also, not because of the restatement, but because it proceeded in such an orderly way, without doubling back. E.g., halfway through (c), there's a sentence starting "We would like to find...", which interrupts the deductive steps to insert an end-goal. It seems unnatural. Even though I chose (a), and like my argument, I find some of the arguments here for (c) convincing as well. I could not proceed farther than question 1, because I'm kind of tired of real analysis at this point. Certainly not on Sunday morning. ;-)
• dhimes 14y ago
  Perhaps they are collecting stats. We should check back later.
• anonymouz 14y ago
  From the post: "I would also be interested in comments about how you came to your judgments. All comments on both experiments and all votes in the polls will be kept private until I decide that it is time to finish the second experiment."
• ubercow13 14y ago
  A lot of people read Gower's blog as it has some really useful expositions of undergraduate maths, which he makes available for anybody who might find them useful. In that sense I think he is justified in not providing a reward; you don't have to do the test if you don't want to anyway. He will no doubt post later with the actual writers' identities.