1. Post #41
    Gold Member
    Watevaman's Avatar
    August 2005
    6,667 Posts
    The people that rate OP dumb have never taken higher level math classes.
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  2. Post #42
    Plastical's Avatar
    August 2009
    583 Posts
    0.999... = 1 is true in the same way that 0.000... = 0.

    It just doesn't look that way because your brain goes:

    .9 =/= 1
    .99 =/= 1
    .999 =/= 1
    .9999 =/= 1

    So it would intuitively follow that no matter how many nines you put, it will never equal 1. The problem is that when you put an infinite number of nines, it equals 1.
    I would like to see an actual proof of this.

  3. Post #43
    Gold Member
    Smashmaster's Avatar
    April 2005
    1,549 Posts
    They're different numbers, it's just that one is only possible (to measure, at least) in theory.
    No, they're the same number. They are both 1. 1 can be measured, and exists. Therefore both exist, and can be measured.
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  4. Post #44
    Huge Faggot #2
    GoldenGnome's Avatar
    November 2007
    5,149 Posts
    0.3 repeating isn't 1/3. It's a decimal APPROXIMATION of 1/3 which means it isn't the exact value (of 1/3). 0.3333 to the infinity * 3 is not the same as 1/3 * 3. One is a multiplication using absolute values while the other is an approximation. They're two different numbers.

    Either that or I'm just too stupid enough to understand why 0.9 repeating is the same as 1.
    it's the second choice i'm afraid :(

  5. Post #45
    Gold Member
    Smashmaster's Avatar
    April 2005
    1,549 Posts
    I would like to see an actual proof of this.
    Jesus, fine. But if you can't understand the math behind the proof, you aren't allowed to rebut it.

    Here's my white-board ghetto-proof.

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  6. Post #46

    April 2011
    64 Posts
    http://en.wikipedia.org/wiki/Numerical_analysis

    Go read it and stop claiming 0.9999.. = 1 ; If u keep doing it, I will hold u accountable the next time a bridge collapses.
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  7. Post #47
    Gold Member
    Smashmaster's Avatar
    April 2005
    1,549 Posts
    http://en.wikipedia.org/wiki/Numerical_analysis

    Go read it and stop claiming 0.9999.. = 1 ; If u keep doing it, I will hold u accountable the next time a bridge collapses.
    You make the mistake of assuming that 0.999... is an approximation. It is not. It is exact. It is exactly 1.
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  8. Post #48
    I AM A PUTRID FUCK WHO CHASES AFTER PEOPLE'S VANS, SCARES GIRLS, FELL FOR A RANDOM FUCK ON THE INTERNET WHO I'VE NEVER EVEN SEEN, AND SHOVED RUSTY NAILS DOWN MY COCK FOR THEM.
    demoniclemon's Avatar
    July 2008
    4,193 Posts
    I wish I was better at math.
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  9. Post #49
    I'm halving my usage of math each week.. but, apparently I'll never be able to quit.
    Bradyns's Avatar
    October 2009
    5,821 Posts
    Jesus, fine. But if you can't understand the math behind the proof, you aren't allowed to rebut it.

    Here's my white-board ghetto-proof.

    You can also use this to show that limit 'n' tends to zero, for 0.00000000........1 = 0
    Convergence on zero.

  10. Post #50

    April 2011
    64 Posts
    You make the mistake of assuming that 0.999... is an approximation. It is not. It is exact. It is exactly 1.
    Touché - my point is wrong
    People simply shouldnt claim that 1/3 * 3 = 0.9999.. - its not
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  11. Post #51
    I remember when titles used to mean something, now you can get one for a dollar, this all used to be fields, get off my lawn damn kids etc.
    evlbzltyr's Avatar
    May 2006
    6,330 Posts
    corrected because I'm an idiot and put numbers where numbers should not have been

    0.333... = 1/3

    0.333... + 0.333... + 0.333... = 0.999...

    0.999... = 3/3

    0.999... = 1
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  12. Post #52
    Gold Member
    Smashmaster's Avatar
    April 2005
    1,549 Posts
    3.333... = 1/3

    3.333... x 3.333... = 9.999...

    9.999... = 3/3

    9.999... = 1

    I'm not great at maths, but that's what someone told me on YouTube, so there we go.
    Besides being late, 3.333... =/= 1/3

    0.333... = 1/3
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  13. Post #53

    April 2011
    64 Posts
    3.333... = 1/3 - WRONG

    3.333... x 3.333... = 9.999... - WRONG

    9.999... = 3/3 - WRONG

    9.999... = 1 - WRONG

    I'm not great at maths, but that's what someone told me on YouTube, so there we go.
    Good job being wrong 4 times in a single post. U just failed math.
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  14. Post #54
    Plastical's Avatar
    August 2009
    583 Posts
    Jesus, fine. But if you can't understand the math behind the proof, you aren't allowed to rebut it.

    Here's my white-board ghetto-proof.

    If I were to solve this in a math test by saying that the limit of 10^n as n approaches -infinity, I would agree with you by saying that the answer infinitely approaches 0, hence the (1 - 0 = 1). However, the problem with the limit method is that it is an approximation of the answer for whatever value of n it is approaching. If I were to use a simple algebraic method, this wouldn't hold.
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  15. Post #55
    Gold Member
    Paramud's Avatar
    November 2008
    9,212 Posts
    3.333... = 1/3

    3.333... x 3.333... = 9.999...

    9.999... = 3/3

    9.999... = 1

    I'm not great at maths, but that's what someone told me on YouTube, so there we go.
    3.333... * 3.333... is actually somewhere around 11.1099999~

  16. Post #56
    acidcj's Avatar
    March 2010
    4,000 Posts
    The people that rate OP dumb have never taken higher level math classes.
    I rated it dumb because it was dumb, and because this thread and threads like it have been made way too many times, not because I disagreed with the fact that 0.99... = 1.

  17. Post #57
    Gold Member
    Smashmaster's Avatar
    April 2005
    1,549 Posts
    If I were to use a simple algebraic method, this wouldn't hold.
    So do it.

  18. Post #58
    ffFf
    Uber|nooB's Avatar
    June 2005
    5,912 Posts
    I'm confused why people are rating the OP dumb.
    because every other thread regarding this topic that has been posted on fp did not end well

    Edited:

    as summed up in the first post:

    Oh god, not this shit again.
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  19. Post #59
    fantafuzz's Avatar
    February 2008
    1,787 Posts
    Isn't the only reason people still dont understand this because they dont understand infinity? If the number of nines is just insanely super mega high, 1 does not equal it, but with infinite nines, 1 does. It's just that people think that infinity is just a really long number, that does end, that can be treated just like other numbers...
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  20. Post #60
    Gold Member
    DesolateGrun's Avatar
    July 2008
    6,268 Posts
    I bet that girls vagina is oozing smegma.
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  21. Post #61
    The Cold Wind Of France
    Dennab
    November 2008
    18,691 Posts
    0.333..... is the decimal representation of the fraction (1/3).

    It's the same thing.
    no, the key word is there

    "representation"

    you'd need an infinite numbers of 3333s, and the more you'd have, the closer you'd get to 1

    it's not the same thing, and that's why the whole 0.999 = 1 is BS
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  22. Post #62
    Plastical's Avatar
    August 2009
    583 Posts
    Would you agree with me that using the limit method that you showed to find the real value is an approximation, good for maybe an explanation in theory but not for a concrete answer? Using simple mathematical operations, if you were to subtract 0.9 to the infinity from 1, you wouldn't get 0 unless you're using an approximation of the value.

  23. Post #63
    MRTW113's Avatar
    March 2010
    4,725 Posts
    shitstorm successful
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  24. Post #64

    April 2011
    64 Posts
    Its simple ...

    1/3 is NOT 0.3333.. ; however, 0.3333... is an APPROXIMATION of 1/3 - it is CLOSE to it
    So doing 0.3333.. * 3 = 0.9999.. - Which is CLOSE to 1 - but its NOT 1!

    And doing 1/3 * 3 = 1 ; which is infact true!
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  25. Post #65
    Gold Member
    Glorbo's Avatar
    May 2010
    5,372 Posts
    the problem with the limit method is that it is an approximation of the answer for whatever value of n it is approaching.
    No it's not. lims give exact answers.

  26. Post #66
    Gold Member
    Smasher 006's Avatar
    September 2009
    4,865 Posts
    I remember there being another rule that applies to this which says that if there is no real number between two 'Numbers', they must be the same as there is literally nothing between them.

  27. Post #67
    Gold Member
    Glorbo's Avatar
    May 2010
    5,372 Posts
    if you were to subtract 0.9 to the infinity from 1, you wouldn't get 0 unless you're using an approximation of the value.
    Yes, you would. I think you don't really grasp the concept of infinity well.
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  28. Post #68
    Plastical's Avatar
    August 2009
    583 Posts
    No it's not. lims give exact answers.
    It depends, in Smashmaster's example, it is one.

  29. Post #69
    Gold Member
    Glorbo's Avatar
    May 2010
    5,372 Posts
    It depends, in Smashmaster's example, it is one.
    What I mean is, lims are never approximates. limits give you precise numbers, whether they are rational or irrational. You choose where to cut them into an approximate.

  30. Post #70
    Gold Member
    Smashmaster's Avatar
    April 2005
    1,549 Posts
    Would you agree with me that using the limit method that you showed to find the real value is an approximation, good for maybe an explanation in theory but not for a concrete answer? Using simple mathematical operations, if you were to subtract 0.9 to the infinity from 1, you wouldn't get 0 unless you're using an approximation of the value.
    I wouldn't. Saying there is a number infinitely close to 1, but not equal to 1, is a contradiction. It's like saying there is an object that is colored entirely red, and colored a little blue. You have to be careful when working with infinity. You can't round infinity, and you can't approximate infinity. If you multiply something by infinity, you get infinity. If you divide by it, you get zero. You don't get 'almost infinity' or 'almost zero.' That's just how it works.

  31. Post #71
    Plastical's Avatar
    August 2009
    583 Posts
    I wouldn't. Saying there is a number infinitely close to 1, but not equal to 1, is a contradiction. It's like saying there is an object that is colored entirely red, and colored a little blue.
    The idea is that the limit value of 10^n as n approaches -infinity tends to 0. I get what you're saying with infinitely approaching 1, but if what you're saying is true, then if you start with 1 and you keep infinitely dividing by 2, you would eventually reach 0. I'm not so sure about that.

  32. Post #72
    Gold Member
    Paramud's Avatar
    November 2008
    9,212 Posts
    It's like saying there is an object that is colored entirely red, and colored a little blue.
    That doesn't actually work, since that would mean saying there's a number that's exactly one, but isn't one.

    You have to be careful when working with infinity. You can't round infinity, and you can't approximate infinity.
    You seem to be doing a fine job of it.

  33. Post #73
    Gold Member
    Aredbomb's Avatar
    July 2009
    3,764 Posts
    shitstorm successful
    Caused by fucking decimals, no less.

  34. Post #74
    I remember when titles used to mean something, now you can get one for a dollar, this all used to be fields, get off my lawn damn kids etc.
    evlbzltyr's Avatar
    May 2006
    6,330 Posts
    Good job being wrong 4 times in a single post. U just failed math.
    Good job being wrong two times in a single post. You just failed English.

    Besides, it was pretty obvious that I'd just made a couple of typos because I wasn't thinking straight. I'm not dumb enough to actually think that 9.999 recurring is equal to one, I meant 0.999 recurring, and accidentally put the number at the beginning instead of a zero. But whatever, this is obviously really important to you all, so I'll just leave you guys to it.
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  35. Post #75
    Gold Member
    Smashmaster's Avatar
    April 2005
    1,549 Posts
    if what you're saying is true, then if you start with 1 and you keep infinitely dividing by 2, you would eventually reach 0. I'm not so sure about that.
    I can prove that it does in 10 different ways. You can't prove that it doesn't in even 1 way.

    realistically speaking Infinity + 2 is greater than infinity although I would understand why you wouldn't accept this answer.
    ∞ + 2 > ∞
    Undefined operation

  36. Post #76
    Gold Member
    Glorbo's Avatar
    May 2010
    5,372 Posts
    The idea is that the limit value of 10^n as n approaches -infinity tends to 0.
    That's because you can't really get to infinity. Saying "I got to infinity" is contradicting yourself, because infinity is defined as a point that you cannot reach no matter how much you add and try. Now, in theory, if you could somehow jump to this magical point called infinity (by maybe advancing an infinite amount of steps at once), you would see that yes, it equals zero.

    My logic goes as this. If I have a chocolate bar, and I want to divide it to an infinite number of people, the only reasonable quantity I can give to anyone is zero, because if I gave any tangible amount, then it will eventually run out before I can divide it equally to everyone. I can't give them an infinitely small piece because it's the same as zero. 0.00000...001 is not infinitely small. Why? Because the fact that I just ended that number with a 1 contradicts my previous statement that it never ends. And if it never ends, then there can't be a number like that.

    My point is, in order for anyone to get some amount, you have to stick that one somewhere, but you can't, because you'll be contradicting yourself.
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  37. Post #77
    Gold Member
    Paramud's Avatar
    November 2008
    9,212 Posts
    I can prove that it does in 10 different ways. You can't prove that it doesn't in even 1 way.
    Please do.

  38. Post #78
    Gold Member
    Smashmaster's Avatar
    April 2005
    1,549 Posts
    Please do.
    And while I work on this, would you please work on your definitive 0.999... =/= 1 proof as well? No? Then I'm not wasting my time.
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  39. Post #79
    Plastical's Avatar
    August 2009
    583 Posts
    -snip-

  40. Post #80
    Gold Member
    Paramud's Avatar
    November 2008
    9,212 Posts
    And while I work on this, would you please work on your definitive 0.999... =/= 1 proof as well? No? Then I'm not wasting my time.
    Educating a waste of time? Teachers everywhere are heartbroken.

    My logic goes as this. If I have a chocolate bar, and I want to divide it to an infinite number of people, the only reasonable quantity I can give to anyone is zero, because if I gave any tangible amount, then it will eventually run out before I can divide it equally to everyone. I can't give them an infinitely small piece because it's the same as zero.
    Actually, you can't give them all a piece of chocolate because eventually you'll get to atoms and if you try to split those equally they'll all die.