.9999999 Is Proven To Be Equal To 1!

Discussion in 'General Discussion' started by Aurori, Sep 12, 2007.

  1. xlink

    xlink GR's Tech Enthusiast

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    no, if he's right then he's right

    1/3 =.3333333333...
    that's a given

    3 * .3 =.9
    3 * .33 =.99
    3 * .333 =.999
    ...
    3*.333recurring=.9999recurring
    3*(1/3)=.9999recurring

    here's the algebraic proof placed into some calcusu based terms

    lim(m --> ∞) sum(n = 1)^m (9)/(10^n) = 1
    0.9999... = 1

    Thus x = 0.9999...
    10x = 9.9999...
    10x - x = 9.9999... - 0.9999...
    9x = 9
    x = 1.

    of course since people here fail to understand the arithmetic proof, and the algebraic proof just goes over their head this probably won't do much...


    and here is a geometric proof of it as defined by a series
    http://www.physicsforums.com/latex_images/67/678504-0.png


    and here's a very simple calc proof

    1[-1/(10^∞)]=.9999999999(recurring)

    so basically 1/(10^∞) would be a decimal with a lot of 0s and a 1 at the end right?



    lim x ->∞ 1/(10^x)=0


    nope? it's 0. 1 divided by ∞=0
     
  2. r3m1x

    r3m1x Well-Known Member

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    You throw a rock at a dude's car. You don't hit dead center on the window...but it still breaks. 0.9 repeating isn't 1...but it's close enough for it to count
     
  3. Flag

    Flag Well-Known Member

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    Your math teachers are retarted.
     
  4. xlink

    xlink GR's Tech Enthusiast

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    no it's 1.

    if you're doing a greatest interger function and you end up with .9recurring as the independant variable and you



    so for f=[[x]]
    f(.9recurring)=1


    that's right it equals 1. if it didn't equal 1 then f(.9recurring) would equal 0.

    there IS mathematical significance to this. in most cases it doesn't matter but there are some cases. If you get a dick of a professor and they include a question like the above on a test, expect a 0 if your answer is 0. it can matter

    f=tan π/(2*[[x]])

    in that case your definition is the difference between "0" and "undefined"

    that's what I get for having a major which requires 3 semesters of upper level calculus and stats...
     
  5. xlink

    xlink GR's Tech Enthusiast

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    that might be the case, but it still doesn't mean that you're any more knowledgeable on the matter. chances are you're not. especially if you don't accept fundamental aspects of math
     
  6. A Spoon

    A Spoon Well-Known Member

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    Just thought I'd point out that one third doesn't equal .333 repeating.
     
  7. xlink

    xlink GR's Tech Enthusiast

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    divide 1/3 manually by hand

    in the standard 10 digit decimal system it does


    if that doesn't work for you then

    1/7=.1428571428...
    +6/7=0.857142857...

    =9/9=.99999999999...



    1/6=.1666666666...
    +5/6=0.833333333...

    =6/6=.99999999999...

    it's true for ANY rational expression FYI.
     
  8. FTWrath

    FTWrath Well-Known Member

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    I'm going to get so much freshmen ass at school with this.
     
  9. Shadowzz

    Shadowzz Member

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    omg confusing?
     
  10. Shadowzz

    Shadowzz Member

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    it so is not.
     
  11. LA-384

    LA-384 Well-Known Member

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    i don't know what is said on page 2-4, but it's nothing more than complete bull----.

    i believe with "repeating" you mean an infinite amount.
    so 0.9999(repeating) would be nothing more then a zero, a dot and then an infinite amount of 9's. Whenever you multiply that by 10, you will get a 0 at the end, no matter how many 9's there are behind the dot, you will never end up with a 9 at the end. That being true, the rest of the calculation is just garbage. So .99999 equals 1 is false unless you start to round off.


    The correct math thingy:

    x=0.99~9 (~ stands for a lot of the same)

    1.) So that would mean that 10x = 9.99~90

    2.) 10x - x = 8,999~91 (9.99~90 - .999~9 = 8,999~91)

    3.) so 9x = 8,999~91

    4.) Which means x = 0,99~9 once it is reduced!
     
  12. Bracketology

    Bracketology Well-Known Member

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    Im sorry you are wrong. You change what x meant in the middle of the equation. o_O
     
  13. Bracketology

    Bracketology Well-Known Member

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    Im sorry you are wrong. You change what x meant in the middle of the equation. o_O
     
  14. FriendlyGuy

    FriendlyGuy Well-Known Member

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    you can't add a zero to the end, its by definition infinite
     
  15. LoCkEdNsEdAtEd

    LoCkEdNsEdAtEd Member

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    woah, seems valid... im gonna ask my teacher about this, hes a total genius O_O
     

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