Happy pi day!!!

Discussion in 'Physics & Math' started by science man, Mar 14, 2010.

  1. Neverfly Banned Banned

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    You have twice run away from debates with me and I may be a bit primitive and not a big brain, myself. I wonder what this says about your ability to support and demonstrate the claims you make?

    You seem to always resort to ad hom attacks when you fail in your arguments.
     
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  3. Jack_ Banned Banned

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    Sorry, your proof does not work.

    Based on the indexing of sets, you must proceed by transfinite induction.

    You did not.

    Please provide a proof based on transfinite induction.

    Thanks.
     
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  5. Jack_ Banned Banned

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    BS.

    I may stop talking to someone out of boredom.

    I will not comment about you.
     
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  7. Jack_ Banned Banned

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    OK, I will talk.

    We are talking about Cantor's diagonally argument.
    This is very important.

    Kurt Godel used this plus Bertrand Russell's liar's paradox to prove his 1st incompleteness theorem.

    Now, this is important because it asserts it is impossible to develop a complete theory of the natural numbers even if you are allowed to supply a countably infinite set of axioms.

    Why is this important?

    Because physics folks have yet to realize unless they can axiomitize the natural numbers, then cannot axiomitize the physical universe since the natural number are a subset of that universe.

    Godel proved the antecedent of the above is impossible.
     
  8. Neverfly Banned Banned

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    3,576
    Aww come on... You know you want me, big boy.

    So you can always use the excuse of ducking out of a debate when your arguments fail and your claims are demonstrated as riddled with fallacy by claiming you GOT BORED?!

    Surely you can come up with a better excuse than that.
    Why suddenly get bored on a topic you took active interest in all the way up to the point where your arguments went kersplat?

    How odd. Perhaps you're too intellectual for us over here and you get bored easily.
     
  9. Vic the Trader straight chillin Registered Senior Member

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    Does the theory of infinity contradict the nature of 1?
     
  10. Jack_ Banned Banned

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    OK, you win, you are a troll.

    :roflmao:
     
  11. Jack_ Banned Banned

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    There is no real theory of infinity.

    There is a set theoretic axiom that postulates or assumes it.

    This is combined with the power set axiom to produce sets of greater cardinality.

    There are three concepts in this area.

    1) Dedekind cuts which by human ingenuity created the irrationals.
    2) Cantor's argument which shows the set of irrationals is strictly greater than the rationals.
    3) The Generalized Continuum Hypothesis which asserts there exists cardinalities greater than the Reals.
     
  12. Neverfly Banned Banned

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    3,576
    Limit Theory

    Please Register or Log in to view the hidden image!


    YAY! I'm a wiener!!!
     
  13. AlphaNumeric Fully ionized Registered Senior Member

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    How in any way did this respond to what he'd said? You asked him to prove that the cardinality of P(N) is strictly larger than the cardinality of N, which he did using Cantor's diagonal method. If you didn't agree with it then say where and why. Is you don't understand it say where.

    Funkstar answered your challenge. If you can't accept it don't bother posting.

    And again, you retort nothing anyone says to you. You lay down a challenge, someone meets it, you can't retort it and so you just say "Wrong!". If you had a justification for saying "Wrong" other than your unwillingness to admit mistakes you'd have given it.

    And its laughable you are calling me primitive. I've already had to explain coordinate geometry and special relativity to you and now you're getting schooled on basic set theory. The fact you keep putting your foot in it when it comes to this stuff demonstrates you haven't ever done any logic and set theory so your use of 'decidability' was nothing more than an attempt to appear more informed than you are.

    Of course if you think I'm wrong and you want to put your maths where your mouth is I'm happy to start a thread so that you can have some input/ make some comments on the work I do. If you believe what you're saying surely you won't turn down an opportunity to put me in my place on material which I consider 'home territory'?

    Oh look, more buzzwords to do with material clearly beyond your understanding.

    This isn't true. Firstly there's more mathematics than physics because physics is about this universe while mathematics can be used to describe our set of laws of nature but also to construct different sets of laws and describe phenomena which don't exist. For instance if the universe isn't 10 or 11 dimensional then string theory obviously isn't a valid model but instead the model of a hypothetical universe which is filled with things much like our own but with a different underling set of principles.

    Secondly physicists and mathematicians have different goals. A mathematician wants to find out all the logical implications of a set of axioms and because he doesn't need experiments or observations and has a framework of logic there is no limit to how far or convoluted or abstract he can go. A physicist is limited by what can be measured. If someone guessed, somehow, the mathematical construct which provides an exact description of nature, ie a theory of everything, it is a ToE because it predicts correctly, to arbitrary accuracy, all phenomenological processes. This would provide the complete description of Nature but you would not need to know the source of the physical postulates. Once you have the ToE you don't need to refine your models. A guessed set of postulates which gives a ToE would not need to be axiomised, in the sense of having some deeper justification, for it to still be science because you measure its success by how much and how accurately it describes the universe. This isn't the case for a mathematician, there is no point at which mathematics is 'finished'.

    Besides, I think its a little silly you telling physicists what they should or shouldn't or could or couldn't be doing since you've made it abundantly clear you have disdain for their work and a misplaced confidence in your knowledge (or lack there of).

    Obviously your belief that its not you whose wrong but everyone else extends beyond just basic undergrad mathematical physics. You lay down challenges, which people met them and when you're asked to do something or answer a simple question you run away or just ignore it. You have mass quoted more than one post in this thread and then just replied with a 1 line comment. You seem to be projecting your trolling onto other people. Why can't you respond to direct questions? Why do you continually believe its everyone else whose wrong and not you?

    If you can't respond to direct questions, asked repeatedly, and you refuse to put your maths where your mouth is, even after other people have, you are trolling. It certainly seems like you're becoming more and more aggressive. Perhaps you're just getting upset everyone keeps correcting you on basic things. But then that's the price you pay when you claim to know things you don't.
     
  14. Jack_ Banned Banned

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    1,383
    Sorry An, up it a bit.

    You are so off base and I do not have the patience to correct you.

    Anyway, I have more intense posts and I will wait for the real players.
     
  15. Jack_ Banned Banned

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    OK, answer #62. With all your verbosity above, you can do this.

    How long will this take?
     
  16. Jack_ Banned Banned

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    Explain in #59 why the poster failed and my argument proved that.

    Hurry, I lack patience for stupidity.
     
  17. funkstar ratsknuf Valued Senior Member

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    Ouch, that's harsh. Could you tell me why you think the beauty is lost? (Bear in mind that I did write it as a quick and dirty response to Jack, so I didn't bother with LaTeX, nor much with exposition.)

    To my mind, it is a proof showing that the powerset of the naturals have greater cardinality than the naturals (using the diagonal method). That's what I was asked to show, and that's what I did. temur pointed out that it easily generalizes to any set, which is certainly true: I deliberately wrote my proof so that there wasn't actually any reliance on any properties of \(\mathbb{N}\): Substitute any set in the place of \(\mathbb{N}\) and the proof still goes through.

    To be a bit brutal in return, I think you in your (vastly more pedagogically oriented) post are somewhat confusing the proof that the reals are uncountably infinite with the proof that the powerset of a set has strictly greater cardinality. There's no need to talk about "lists of numbers" when just proving that \(|\mathbb{N}| < |\mathcal{P}(\mathbb{N})|\).

    But I agree with you that the diagonal argument is one of the most important and beautiful proof methods in all of mathematics. It's used all the time in computer science, as well.
     
  18. oh transcendentals are irrationals that are not shown as a number to begin with. Even though they are but not visually shown as a number. correct?
     
  19. funkstar ratsknuf Valued Senior Member

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    I'm sorry, was there an argument somewhere in there?

    Of course, there is such a surjection \(S\): Let \(S(n) = 2n +1\) (assuming that \(0 \in \mathbb{N}\), else just put a minus there).

    Now what?
     
  20. Jack_ Banned Banned

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    1,383
    yea, your argument does not exclude this logic of the odd and even numbers.

    Hence, you did not prove the continuum.

    Why do I have to explain this to you?
     
  21. Neverfly Banned Banned

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    No.
    That excuse is a very lame cop out. Meet the challenges or lay none of your own.
    You keep doing this-- running away and making excuses. It's truly pathetic.
    If you had half the mathematical knowledge you are Pretending you have, you would be well aware that you are mistaken. Instead, you try to play it off as if everyone else is wrong but they bore you so much you cannot be bothered to correct them.

    No. You must Support Your Arguments or retract them.

    Otherwise, your claims are unsupported and you present Nothing Of Value.
    YOU explain how he failed as I see no failure there. I see failure in your posts... and then I see cop outs where you fail to demonstrate anything mathematically. You seem to be so busy pretending to understand the math, you cannot keep up with your illusions and must duck and hide instead.

    Calling others stupid? Do you Really Think the readers are actually buying into your bs at all?
     
  22. funkstar ratsknuf Valued Senior Member

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    1,390
    Again, are those sentences intended to convey actual meaning? Or are you merely flinging random words together in the hope that you might fool the casual onlooker?
    You couldn't explain your way out of a wet paper bag.
     
  23. AlphaNumeric Fully ionized Registered Senior Member

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    Its clear to everyone else that you don't have the knowledge and ability to correct me (assuming I'm even wrong). You've replied with one line responses, mass quoting and then ignoring other people, too many times in this thread now and its all too obvious to everyone you've all talk with nothing to say.

    I offered to start a dedicated through where you and I can talk about some of the kind of mathematics I do day to day. If you're 'a real player' and I'm not surely you'd have no problem demonstrating to all of us your knowledge? Because you sure haven't done it here.

    You lack understanding and its clear you've bitten off more than you can chew, as all the people in this thread other than you have come to the same conclusion about you, that you're a BS'er.

    Explain how the nature of the odd and even numbers have anything to do with the issue of proving the continuum? I asked you this before and you ignored me. Now Funkstar has asked you too, having made a similar comment as I did, that you appear to have no understanding of the words you use.

    I really don't get why you'd enter into a discussion with several people on a topic you don't know and they do and yet you repeatedly attempt to correct them. Surely you know all you'll do is come across as an idiot. Congratulations, mission accomplished.
     

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