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nincompoop Group Title

when is a mathematical proof not a proof?

  • one year ago
  • one year ago

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  1. UsukiDoll Group Title
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    when there's no solution or when the proof doesn't make sense. That's uh my guess.

    • one year ago
  2. zzr0ck3r Group Title
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    this is a contradiction a^-a thus a mathematical proof will never not be a proof.

    • one year ago
  3. estudier Group Title
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    False premise, true conclusion?

    • one year ago
  4. miteshchvm Group Title
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    when the statement is an axiom

    • one year ago
  5. zzr0ck3r Group Title
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    axioms can be proved

    • one year ago
  6. estudier Group Title
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    If you can prove an axiom, it isn't an axiom....

    • one year ago
  7. zzr0ck3r Group Title
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    this is tantamount to asking when is 2 not equal to 2

    • one year ago
  8. zzr0ck3r Group Title
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    either way, something cant be both true and false at the same time, and this is what the question asks

    • one year ago
  9. UnkleRhaukus Group Title
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    when you are proving something is false

    • one year ago
  10. zzr0ck3r Group Title
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    still a proof...

    • one year ago
  11. estudier Group Title
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    When it is a valid proof but not yet accepted by the mathematical community. Or accepted as valid but wrongly.

    • one year ago
  12. zzr0ck3r Group Title
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    am I reading this question wrong? anyone? explain why, what I'm saying, is not the only logical answer?

    • one year ago
  13. estudier Group Title
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    Logically, p and not p is a bad thing (obviously) I am sure that is not the intention behind the question.....(maybe)

    • one year ago
  14. tanvidais13 Group Title
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    TOK ALERT.

    • one year ago
  15. zzr0ck3r Group Title
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    hmm, I disagree. I think if someone is just learning about proofs... a question involving a contradiction seems like an obvious one to ask a student.

    • one year ago
  16. estudier Group Title
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    A proof not yet 100% accepted by the mathematical community..

    • one year ago
  17. badreferences Group Title
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    Bertrand Russell's "Principia Mathematica" is a relevant book. It deals with the construction of what a mathematical proof is. Mathematical proofs are constructed using objects, maps, and equivalences. Maps are relationships between objects. Objects are defined to have properties. Equivalences are to determine what we can say are the "same". A contradiction usually doesn't pass under mathematics, but it works in fuzzy logic and paraconsistent mathematics. (For a famous example, Godel's incompleteness theorems on the extendability of arithmetic axioms.) So, in short, what passes as a mathematical proof is technically what mathematicians have agreed on to make sense. The equivalences might have Platonic existence outside of this agreement, in which case the mathematicians have made a mistake; but in the end, instrumentally it is the intuition that decides what can be called the same. But this doesn't mean that you can just run around making any proof you want. There is still a lot of technical subtlety, and as you learn mathematics you will create ad hoc modifiers to what constitutes a good proof. You will have different levels of rigor for different kinds of proofs, because in the end, we're looking for math to be intellectually useful. But, in short, if you're given that \(A=B\), a strong heuristic is that any map on \(A\to C(A)\) should also map as \(B\to C(B)\). And by "strong heuristic", I mean it is right in virtually every scenario except for the most contrived, philosophically demanding ones.

    • one year ago
  18. estudier Group Title
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    http://en.wikipedia.org/wiki/Close-packing_of_equal_spheres

    • one year ago
  19. zzr0ck3r Group Title
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    If it is not accepted by the Mathematical community, it is not a proof, so something cant be a proof unless its accepted by the mathematical community. So we still have a contradiction, even by your definition...

    • one year ago
  20. badreferences Group Title
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    An addendum, the contradiction paradox is usually a good way of determining falsehood, but as has been demonstrating by the "quantum eraser" experiment http://grad.physics.sunysb.edu/~amarch/ you need to be careful about what constitutes a contradiction. @zzr0ck3r You aren't reading what I wrote clearly enough.

    • one year ago
  21. estudier Group Title
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    Hum... a proof has no independant (ie logical) existance?

    • one year ago
  22. badreferences Group Title
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    @estudier We call that Platonic existence. It might, but this is up to a lot of debate.

    • one year ago
  23. badreferences Group Title
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    Bertrand Russell, Plato, and many modern mathematicians believe it does, but in a form we don't know of yet. Wittgenstein, Hume, Kant, and the peerless mathematician Godel (along with plenty, but not the majority, of Ivy mathematicians) believe that it doesn't.

    • one year ago
  24. estudier Group Title
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    I don't agree that this is a case of Platonistic argument (which I don't subscribe to).

    • one year ago
  25. badreferences Group Title
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    Go on? Platonic existence is defined as something that can be objectively verified in the most extreme of cases no matter what (generally, I'm a bit rusty). This seems to me to be a clear cut case of what constitutes a proof. I won't press my own views, I'm just giving names to read. What they have to say is much better than what I do.

    • one year ago
  26. estudier Group Title
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    A proof is a logical binding together of possibly Platonic mathematical objects but not such an object itself.

    • one year ago
  27. zzr0ck3r Group Title
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    Well, I don't think I can pretend to know enough about quantum theory to understand what this all means, but I have a new answer. A proof is not a proof when know one is there to witness the proof.

    • one year ago
  28. zzr0ck3r Group Title
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    If it is a very small proof...

    • one year ago
  29. estudier Group Title
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    One hand clapping.....

    • one year ago
  30. badreferences Group Title
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    This is true, but a proof is also constrained by axioms, which are maps.

    • one year ago
  31. estudier Group Title
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    @nincompoop Why are you deleting your posts?

    • one year ago
  32. badreferences Group Title
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    He's a ninja.

    • one year ago
  33. badreferences Group Title
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    Of course, a disclaimer is that I'm not a philosopher, and this is veering very close to philosophy, so I might've just been misinterpreting all the books I've read. :P

    • one year ago
  34. zzr0ck3r Group Title
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    This is only philosophy. :)

    • one year ago
  35. UnkleRhaukus Group Title
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    is an incomplete proof a proof?

    • one year ago
  36. UsukiDoll Group Title
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    ummm no?

    • one year ago
  37. jhonyy9 Group Title
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    so i like answering your question with an oder question : when a thesis is not a thesis ? so just till not is proven ,because till not get an accepted proof so till then is just a conjecture this is OK ?

    • one year ago
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