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  1. #126
    Ancient Orator leehuan's Avatar
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    Re: Interesting mathematical statements

    This isn't exactly an interesting maths statement but more or less something I found humourous.

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    -insert title here- Paradoxica's Avatar
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    Re: Interesting mathematical statements

    Quote Originally Posted by leehuan View Post
    This isn't exactly an interesting maths statement but more or less something I found humourous.
    that is rather amusing.

    I have seen people do the same for exponential limits.
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

  3. #128
    -insert title here- Paradoxica's Avatar
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    Re: Interesting mathematical statements

    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

  4. #129
    Ancient Orator leehuan's Avatar
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    Re: Interesting mathematical statements

    Carmichael's theorem:

    Last edited by leehuan; 19 Jan 2016 at 11:17 PM.

  5. #130
    Executive Member KingOfActing's Avatar
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    Re: Interesting mathematical statements

    I don't know if anyone's posted this yet:
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    Re: Interesting mathematical statements

    Quote Originally Posted by leehuan View Post
    Carmichael's theorem:

    Any EARLIER Fibonacci number.

    It wouldn't make any sense without that word.

  7. #132
    -insert title here- Paradoxica's Avatar
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    Re: Interesting mathematical statements

    Quote Originally Posted by KingOfActing View Post
    I don't know if anyone's posted this yet:
    Then the computational extension of the theorem is as follows:

    If a (turing complete) machine can decide whether or not any given input will halt or not, then said machine cannot decide the input comprising itself.

    By the law of the excluded middle, this is a contradiction, and as such, any such machine cannot possibly exist.
    KingOfActing likes this.
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

  8. #133
    Señor Member GoldyOrNugget's Avatar
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    Re: Interesting mathematical statements

    Quote Originally Posted by Paradoxica View Post
    Then the computational extension of the theorem is as follows:

    If a (turing complete) machine can decide whether or not any given input will halt or not, then said machine cannot decide the input comprising itself.

    By the law of the excluded middle, this is a contradiction, and as such, any such machine cannot possibly exist.
    I don't think this statement is quite true. Specifically, the "input comprising itself" bit - I don't know of a proof that shows that this is the case. If you're alluding to the diagonalisation argument, the result is slightly more complex.

    Suppose that A is a Turing machine that given any machine T and input I, decides whether B halts on I.

    Let C be a machine that, when given I, calls A with machine I and input I and halts iff A concludes that I doesn't halt on input I.

    If A is called with machine C and input C and halts, then that means that A must halt on C when given C. Inversely if A is called with (C, C) and doesn't halt, then that means A must halt on (C, C). Here lies the contradiction. (unless I've made a mistake)

    So C is the input that breaks T, not T. Unless I've misunderstood what you've said.

    But the more important question is - who are you? What kind of high school kid has this kind of background in maths? Where did you learn this stuff?
    kawaiipotato likes this.

  9. #134
    Executive Member KingOfActing's Avatar
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    Re: Interesting mathematical statements

    Quote Originally Posted by GoldyOrNugget View Post
    I don't think this statement is quite true. Specifically, the "input comprising itself" bit - I don't know of a proof that shows that this is the case. If you're alluding to the diagonalisation argument, the result is slightly more complex.

    Suppose that A is a Turing machine that given any machine T and input I, decides whether B halts on I.

    Let C be a machine that, when given I, calls A with machine I and input I and halts iff A concludes that I doesn't halt on input I.

    If A is called with machine C and input C and halts, then that means that A must halt on C when given C. Inversely if A is called with (C, C) and doesn't halt, then that means A must halt on (C, C). Here lies the contradiction. (unless I've made a mistake)

    So C is the input that breaks T, not T. Unless I've misunderstood what you've said.

    But the more important question is - who are you? What kind of high school kid has this kind of background in maths? Where did you learn this stuff?
    He's more gay for maths than leehuan
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  10. #135
    Ancient Orator leehuan's Avatar
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    Re: Interesting mathematical statements

    Quote Originally Posted by KingOfActing View Post
    He's more gay for maths than leehuan
    Oi!

  11. #136
    -insert title here- Paradoxica's Avatar
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    Re: Interesting mathematical statements

    Quote Originally Posted by GoldyOrNugget View Post
    I don't think this statement is quite true. Specifically, the "input comprising itself" bit - I don't know of a proof that shows that this is the case. If you're alluding to the diagonalisation argument, the result is slightly more complex.

    Suppose that A is a Turing machine that given any machine T and input I, decides whether B halts on I.

    Let C be a machine that, when given I, calls A with machine I and input I and halts iff A concludes that I doesn't halt on input I.

    If A is called with machine C and input C and halts, then that means that A must halt on C when given C. Inversely if A is called with (C, C) and doesn't halt, then that means A must halt on (C, C). Here lies the contradiction. (unless I've made a mistake)

    So C is the input that breaks T, not T. Unless I've misunderstood what you've said.

    But the more important question is - who are you? What kind of high school kid has this kind of background in maths? Where did you learn this stuff?
    That's why I said comprising. There are a few gaps that I wasn't bothered filling in, because I know the input requires two machines in order to break the supposed machine.
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

  12. #137
    Señor Member GoldyOrNugget's Avatar
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    Re: Interesting mathematical statements

    Quote Originally Posted by Paradoxica View Post
    That's why I said comprising. There are a few gaps that I wasn't bothered filling in, because I know the input requires two machines in order to break the supposed machine.
    You're an IMO guy/girl aren't you?

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    -insert title here- Paradoxica's Avatar
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    Re: Interesting mathematical statements

    Quote Originally Posted by GoldyOrNugget View Post
    You're an IMO guy/girl aren't you?
    If only I were...
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

  14. #139
    ремове кебаб wannaspoon's Avatar
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    Re: Interesting mathematical statements

    Quote Originally Posted by turntaker View Post
    -1 x -1 = 2
    actually = 1, but anyway

  15. #140
    Taking a break! dan964's Avatar
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    Re: Interesting mathematical statements


  16. #141
    Ancient Orator leehuan's Avatar
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    Re: Interesting mathematical statements


  17. #142
    -insert title here- Paradoxica's Avatar
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    Re: Interesting mathematical statements

    Quote Originally Posted by leehuan View Post
    that's not very interesting.

    it's a fairly trivial consequence of Stirling's Approximation... and Limits...
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

  18. #143
    Ancient Orator leehuan's Avatar
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    Re: Interesting mathematical statements

    Too bad, cause even simple things like the power series for exp are interesting when you first see it.

    (Also it was not a consequence in my homework. It was an intermediate step to GET to Stirling's approximation)

  19. #144
    -insert title here- Paradoxica's Avatar
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    Re: Interesting mathematical statements

    Quote Originally Posted by leehuan View Post
    Too bad, cause even simple things like the power series for exp are interesting when you first see it.

    (Also it was not a consequence in my homework. It was an intermediate step to GET to Stirling's approximation)
    I know. But I'm not the one doing it, so ¯\_(ツ)_/¯
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

  20. #145
    This too shall pass Sy123's Avatar
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    Re: Interesting mathematical statements





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    Senior Member sida1049's Avatar
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    Re: Interesting mathematical statements

    Quote Originally Posted by Sy123 View Post




    It is as if you're trying to make our boys Uri and Daniel proud at the same time
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    Bachelor of Science (Advanced Mathematics) III, USYD

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