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Let's discuss Mathematics

Discussion in 'Science & Technology' started by ParadigmShifter, Mar 16, 2009.

  1. ParadigmShifter

    ParadigmShifter Random Nonsense Generator

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    I guess, I submitted to peer review and you found a flaw that's all ;)

    I won't bother posting my proof of the Riemann Conjecture then :lol:
     
  2. Mise

    Mise isle of lucy

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    Physicists take 5 minutes to get the right answer, Mathematicians take 20 minutes to get the wrong answer?
     
  3. dutchfire

    dutchfire Deity Retired Moderator

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    Wait, you can also express it as 7+sumn=1->5 (12n-n^2)(6-n)/216
     
  4. ParadigmShifter

    ParadigmShifter Random Nonsense Generator

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    Hey I'm out of practice it's 15 years since I finished my degree:old:
     
  5. Atticus

    Atticus Deity Retired Moderator

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    That's the topic of numerous jokes told in maths and physics departments all around the world. Typical for these jokes is that only mathematicians and physicists find them amusing (and usually not even them, and that's what makes them funny, little like dirty limericks).

    I'll reproduce one of them which I heard when I was a student:

    Engineer's, physicist's and mathematician's houses caught fire in the middle of the night and all three woke up when the alarm went off. The engineer took the hose and extinguished the fire generously causing bad water damages to his apartment. The physicists in his apartment calculated the exact amount of water needed for the job, and extuinguished the fire. The mathematician woke up, said "solution exists for the problem", and went back to sleep.

    EDIT:
    Yes! Why do have to be so negative Dutchfire? Why do you seek flaws in other people's proofs and not what's good in them?

    EDIT2: Just in case somebody missed it, with no smileys and so on, the EDIT#1 was a joke...
     
  6. Ammar

    Ammar King

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    What sort of degree do you have by the way?
     
  7. ParadigmShifter

    ParadigmShifter Random Nonsense Generator

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    Maths, first year pure/applied/stats, 2nd year pure/stats, 3rd pure only.
     
  8. Gooblah

    Gooblah Heh...

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    We just finished DeMoivre's Theorem in school a few weeks ago. The idea that e ^ (ipi) + 1 = 0 is pretty sweet. However, a proof was not included, sadly.
     
  9. ParadigmShifter

    ParadigmShifter Random Nonsense Generator

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    Well e^it is

    cos t + i sin t

    (by the Taylor expansion of e^x, and by looking at the expansions for sin, cos)

    so with t = pi we have

    e^i*pi = cos pi + i sin pi
    = -1 + 0

    and the result follows.
     
  10. sanabas

    sanabas Psycho Bunny Hall of Fame Staff

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    I sat down across the street to watch it burn, what does that make me?
     
  11. ParadigmShifter

    ParadigmShifter Random Nonsense Generator

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    A reporter?
     
  12. Truronian

    Truronian Quite unfamiliar Retired Moderator

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    A chemist?
     
  13. dutchfire

    dutchfire Deity Retired Moderator

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    That would be if you set it on fire yourself.
     
  14. sanabas

    sanabas Psycho Bunny Hall of Fame Staff

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    Hmm. I think I'll decide I woke up, said 'solution doesn't exist for the problem' and so sat down across the street. Which puts me safely in the mathematician class.
     
  15. ParadigmShifter

    ParadigmShifter Random Nonsense Generator

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    The Banach-Tarski paradox was mentioned in the quiz thread. Is it evidence against the axiom of choice or do the 'impossible' fractal dissections (i.e. can't be done with real matter) make it meaningless for real-world discussion?
     
  16. dutchfire

    dutchfire Deity Retired Moderator

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    Well, I don't really know enough about this to really argue either way, but it seems to me that using it can't really hurt in most cases.
     
  17. Atticus

    Atticus Deity Retired Moderator

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    Some do consider it as a counter-evidence. Most of the people don't really care about it, usually they say it's impossible in real word to cut things so finely, and the parts are nonmeasurable anyways. Latter explanation isn't very good, since it doesn't really explain the paradox.

    As far as I know, BT-paradox is the best intuitive argument against the axiom of choice, which on the other hand is pretty much universally accepted. Much of the best known and most powerful theorems rely on it, Hahn-Banach and Radon-Nikodym to name few (they might be provable otherwise, but not as easily), so life without it would be nasty, brutish and short.

    Often people use it even without noticing it. Imagine how hard it woud be to teach evertybody new maths without axiom of choice.
     
  18. LulThyme

    LulThyme King

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    A related well-known joke:
    "The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?"
     
  19. LulThyme

    LulThyme King

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    You don't need the axiom of choice that often at all in "basic" mathematics. For example, you don't need it when "choosing" from a finite set.

    People in non-math majors probably never see a result that depends on the axiom of choice and math majors probably might only see a few in say 3rd or 4th year of undergrad (usually related to Zorn's Lemma)
     
  20. ParadigmShifter

    ParadigmShifter Random Nonsense Generator

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    Every vector space has a basis (specifically, infinite-dimensional ones) is probably the most important result. I think we assumed fi-di when proving it in 1st year undergrad algebra however.
     

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