.99 Repeating = 1

I_Gorged_Your_MomI_Gorged_Your_Mom Join Date: 2003-10-01 Member: 21361Banned, Constellation
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Comments

  • SwiftspearSwiftspear Custim tital Join Date: 2003-10-29 Member: 22097Members
    Only if you're not trucating <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html//emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo-->
  • OttoDestructOttoDestruct Join Date: 2002-11-08 Member: 7790Members
    int number = 0.99;

    Doesn't work.
  • CabooseCaboose title = name(self, handle) Join Date: 2003-02-15 Member: 13597Members, Constellation
    <u>.99</u> = <u>.99</u>

    plain and simple. It is as close to being 1 as you can get without being 1, but it's not 1.
  • Cereal_KillRCereal_KillR Join Date: 2002-10-31 Member: 1837Members
    edited June 2004
    0.99999999 going to infinity IS = 1....


    seeing as how 10x 0.99999999 = 9.99999999 (all going to infinity)


    9x 0.99999999 = 10x 0.99999999 - 0.99999999
    9x 0.99999999 = 9.99999999 - 0.99999999
    9x 0.99999999 = 9
    0.99999999 = 1


    edit: this is considering you are going all the way to infinity and never stopping. This is due to the fact there is no "last decimal."
    This cannot be done by a computer which actually goes really far but still stops at a given point.
  • I_Gorged_Your_MomI_Gorged_Your_Mom Join Date: 2003-10-01 Member: 21361Banned, Constellation
    To prove: 0.9 repeating = 1

    [proof follows below]

    1. let x = 0.9 repeating
    2. multiply each side by ten, giving

    10x = 9.9 repeating

    3. subtract x from the left, 0.9 repeating
    from the right, giving

    9x = 9

    4. divide both by nine, giving

    x = 1

    5. yet x = 0.9 repeating
    6. therefore

    0.9 repeating = 1
  • OttoDestructOttoDestruct Join Date: 2002-11-08 Member: 7790Members
    <!--QuoteBegin-I Gorged Your Mom+Jun 19 2004, 07:20 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (I Gorged Your Mom @ Jun 19 2004, 07:20 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> To prove: 0.9 repeating = 1

    [proof follows below]

    1. let x = 0.9 repeating
    2. multiply each side by ten, giving

    10x = 9.9 repeating

    3. subtract x from the left, 0.9 repeating
    from the right, giving

    9x = 9

    4. divide both by nine, giving

    x = 1

    5. yet x = 0.9 repeating
    6. therefore

    0.9 repeating = 1 <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
    If I wanted to I could say 8933490320 + 9040340348993488934983498 = 1 like that.
  • RatonetwothreetwooneRatonetwothreetwoone Join Date: 2004-03-23 Member: 27504Members
    i dont think i belong in here

    /me backs out slowly
  • I_Gorged_Your_MomI_Gorged_Your_Mom Join Date: 2003-10-01 Member: 21361Banned, Constellation
  • Cereal_KillRCereal_KillR Join Date: 2002-10-31 Member: 1837Members
    <!--QuoteBegin-OttoDestruct+Jun 20 2004, 02:22 AM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (OttoDestruct @ Jun 20 2004, 02:22 AM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> <!--QuoteBegin-I Gorged Your Mom+Jun 19 2004, 07:20 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (I Gorged Your Mom @ Jun 19 2004, 07:20 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> To prove: 0.9 repeating = 1

    [proof follows below]

    1. let x = 0.9 repeating
    2. multiply each side by ten, giving

    10x = 9.9 repeating

    3. subtract x from the left, 0.9 repeating
    from the right, giving

    9x = 9

    4. divide both by nine, giving

    x = 1

    5. yet x = 0.9 repeating
    6. therefore

    0.9 repeating = 1 <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
    If I wanted to I could say 8933490320 + 9040340348993488934983498 = 1 like that. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
    no you can't. One is mathematically correct, the other wouldn't be. <!--emo&:D--><img src='http://www.unknownworlds.com/forums/html//emoticons/biggrin.gif' border='0' style='vertical-align:middle' alt='biggrin.gif' /><!--endemo-->
  • NumbersNotFoundNumbersNotFound Join Date: 2002-11-07 Member: 7556Members
    1/3rd = .3333333333333333
    2/3rds = .666666666666666
    3/3rds = .999999999999999
  • UnderDOGUnderDOG Join Date: 2003-04-05 Member: 15221Members
    .99 repeating an infite number of times is technicly one, but if you ever stop, and there is a definative number of nines, then it no longer equals one.
  • I_Gorged_Your_MomI_Gorged_Your_Mom Join Date: 2003-10-01 Member: 21361Banned, Constellation
    so then everyone here must agree that .<u>99</u>=1.
  • DOOManiacDOOManiac Worst. Critic. Ever. Join Date: 2002-04-17 Member: 462Members, NS1 Playtester
    Anything between .9999 and 1 is = 1. Otherwise you have too much time on your hands to worry about that sort of crap. Go do something. :P
  • BlackMageBlackMage [citation needed] Join Date: 2003-06-18 Member: 17474Members, Constellation
    0.33333333333333 (off to infinity) is close to 1/3
    0.66666666666666 (off to infinity) is close to 2/3
    0.99999999999999 (off to infinity) is close to 3/3 and close to 1

    you forget one thing, 0.<u>333</u> is unattainable by the defenition of infinity and can only be defined as 1/3
  • [WHO]Them[WHO]Them You can call me Dave Join Date: 2002-12-11 Member: 10593Members, Constellation
    You can't do such a simplistic proof on an infinite quantity, the math simply breaks down.

    It's the same concept as a limit, you never actually get to 1, just really... reallly.... really close.


    0.9999.... is a concept, not a real number. The same as infinity is a concept.
  • BlackMageBlackMage [citation needed] Join Date: 2003-06-18 Member: 17474Members, Constellation
    <!--QuoteBegin-[WHO]Them+Jun 19 2004, 07:59 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> ([WHO]Them @ Jun 19 2004, 07:59 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> You can't do such a simplistic proof on an infinite quantity, the math simply breaks down.

    It's the same concept as a limit, you never actually get to 1, just really... reallly.... really close.


    0.9999.... is a concept, not a real number. The same as infinity is a concept. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
    that's what i said, but less algebraic
  • SurgeSurge asda4a3sklflkgh Join Date: 2002-07-14 Member: 944Members
    edited June 2004
    <!--QuoteBegin-I Gorged Your Mom+Jun 19 2004, 11:13 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (I Gorged Your Mom @ Jun 19 2004, 11:13 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> . <u>99</u> = 1 <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
    That's incorrect. That's like saying pi = 3.14159265, which is incorrect. Pi = Pi. Like how you can't write the square root of 2 accurately. Accurately, the square root of 2 is the square root of 2.
  • [WHO]Them[WHO]Them You can call me Dave Join Date: 2002-12-11 Member: 10593Members, Constellation
    <!--QuoteBegin-I Gorged Your Mom+Jun 19 2004, 05:20 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (I Gorged Your Mom @ Jun 19 2004, 05:20 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->To prove: 0.9 repeating = 1

    [proof follows below]

    1. let x = 0.9 repeating
    2. multiply each side by ten, giving

    10x = 9.9 repeating

    3. subtract x from the left, 0.9 repeating
    from the right, giving

    9x = 9

    4. divide both by nine, giving

    x = 1

    5. yet x = 0.9 repeating
    6. therefore

    0.9 repeating = 1<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
    I'm bored, so here's your counter-proof (I finally get to put my group theory studies to use, w00t)

    If you plan to create your own field (in the group theory sense of the term), then what you said totally works. But In the real number field that most the rest of the world uses, every number has an additive inverse. Since you fail to explicitly define your conceptual number, we'll need to implicitly define it's additive inverse...

    Let N be your conceptual number 0.<u>99999</u>
    Let S be N's additive inverse.

    S <i><b>must</b></i> satisfy the following property.... N + S = 1


    So, let's rewrite your proof a bit so that it actually makes some sense.

    1. N = (1 - S)
    2. 10(N) = 10(1 - S)
    10N = 10 - 10S

    3. 10N - N = (10 - 10S) - (1 - S)
    9N = 9 - 9S

    4. N = 1 - S
    5-6. N = N


    Learned nothing, gained nothing.
  • 7Bistromath7Bistromath Join Date: 2003-12-04 Member: 23928Members, Constellation
    [WHO]Them should go to the Constie forum more often so he can free us from the oppressive .<u>99</u>=1ish-ness of the great and terrible I Gorged Your Mom.
  • JefeJefe Join Date: 2003-04-21 Member: 15734Members, Constellation
    <!--QuoteBegin-I Gorged Your Mom+Jun 19 2004, 06:20 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (I Gorged Your Mom @ Jun 19 2004, 06:20 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> 3. subtract x from the left, 0.9 repeating
    from the right, giving

    9x = 9 <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
    Can you find what's wrong with this picture?
  • MantridMantrid Lockpick Join Date: 2003-12-07 Member: 24109Members
    The whole .99... = 1 phenomenon is more of a philosophical matter rather than an algebraic, mainly because it forces you to try and accept two things that are mutually exclusive and yet both true at the same time. It also deals with a metaphysical aspect in that something incomplete is the same as a whole.
  • JefeJefe Join Date: 2003-04-21 Member: 15734Members, Constellation
    <!--QuoteBegin-Cereal_KillR+Jun 19 2004, 06:25 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (Cereal_KillR @ Jun 19 2004, 06:25 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> <!--QuoteBegin-OttoDestruct+Jun 20 2004, 02:22 AM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (OttoDestruct @ Jun 20 2004, 02:22 AM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> <!--QuoteBegin-I Gorged Your Mom+Jun 19 2004, 07:20 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (I Gorged Your Mom @ Jun 19 2004, 07:20 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> To prove: 0.9 repeating = 1

    [proof follows below]

    1. let x = 0.9 repeating
    2. multiply each side by ten, giving

    10x = 9.9 repeating

    3. subtract x from the left, 0.9 repeating
    from the right, giving

    9x = 9

    4. divide both by nine, giving

    x = 1

    5. yet x = 0.9 repeating
    6. therefore

    0.9 repeating = 1 <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
    If I wanted to I could say 8933490320 + 9040340348993488934983498 = 1 like that. <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
    no you can't. One is mathematically correct, the other wouldn't be. <!--emo&:D--><img src='http://www.unknownworlds.com/forums/html//emoticons/biggrin.gif' border='0' style='vertical-align:middle' alt='biggrin.gif' /><!--endemo--> <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
    Yes you can.


    Just divide the left side by 8933490320 + 9040340348993488934983498 and the right side by 1 SEE HOW SIMPLE IT IS
  • POOP_AkiraPOOP_Akira Join Date: 2003-11-23 Member: 23468Members
    Umm... Whats a 9?

    *head explodes*
  • I_Gorged_Your_MomI_Gorged_Your_Mom Join Date: 2003-10-01 Member: 21361Banned, Constellation
    edited June 2004
    You have to devide them both by the same number, not one 21411513515 and they other 1.

    In the proof, x= .<u>99</u>
  • Soylent_greenSoylent_green Join Date: 2002-12-20 Member: 11220Members, Reinforced - Shadow
    edited June 2004
    <!--QuoteBegin--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> </td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->
    Yes you can.


    Just divide the left side by 8933490320 + 9040340348993488934983498 and the right side by 1 SEE HOW SIMPLE IT IS<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->

    He isn't using circular logic, you are. He first defines x = 0.9999..., this is not what he is trying to prove. You can allways multiply, divide, add or subtract a number from both sides if you wish, this changes nothing if they are equal, and per definition we know x = 0.999.... . If you try to emulate his proof(which among others [who]them has allready showed isn't water tight due to other subtleties with infinites) you get this:

    <i>2.</i> 10x = 10(8933490320 + 9040340348993488934983498)

    <i>3.</i> 9x = 9(8933490320 + 9040340348993488934983498)

    <i>4.</i> x = 8933490320 + 9040340348993488934983498

    <i>5.</i> yet x = 8933490320 + 9040340348993488934983498

    <i>6.</i> therefor 8933490320 + 9040340348993488934983498 = 8933490320 + 9040340348993488934983498

    So, you proved nothing and your back where you started unless you use an infinitely repeating decimal number.
  • Cold_NiTeCold_NiTe Join Date: 2003-09-15 Member: 20875Members
    edited June 2004
    <!--QuoteBegin-[WHO+--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> ([WHO)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->Them,Jun 19 2004, 08:36 PM] <!--QuoteBegin-I Gorged Your Mom+Jun 19 2004, 05:20 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (I Gorged Your Mom @ Jun 19 2004, 05:20 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->
    1. let x = 0.9 repeating
    2. multiply each side by ten, giving

    10x = 9.9 repeating

    3. subtract x from the left, 0.9 repeating
    from the right, giving

    9x = 9

    4. divide both by nine, giving

    x = 1
    <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
    Let N be your conceptual number 0.<u>99999</u>
    Let S be N's additive inverse.

    S <i><b>must</b></i> satisfy the following property.... N + S = 1


    So, let's rewrite your proof a bit so that it actually makes some sense.

    1. N = (1 - S)
    2. 10(N) = 10(1 - S)
    10N = 10 - 10S

    3. 10N - N = (10 - 10S) - (1 - S)
    9N = 9 - 9S

    4. N = 1 - S
    5-6. N = N


    Learned nothing, gained nothing. <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
    I think [WHO]Them has got you there Gorged.

    This being the most important part:
    <!--QuoteBegin--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> </td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->3. 10N - N = (10 - 10S) - (1 - S)
    9N = 9 - 9S

    4. N = 1 - S
    5-6. N = N<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->

    I don't think you can do this as well:
    <!--QuoteBegin--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> </td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->3. subtract x from the left, 0.9 repeating
    from the right, giving<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
    Mathmatically, you can't interchange the variable if the variable is what you are proving, I think... Hmm I'm not so certain now. Oh well, you get the idea.
  • B33FB33F Join Date: 2002-11-19 Member: 9362Members
    Think like a lazy engineer: .9 is close enough to 1.

    <a href='http://www.phy.ilstu.edu/~rfm/EPMjokes.html' target='_blank'>http://www.phy.ilstu.edu/~rfm/EPMjokes.html</a>
  • pardzhpardzh Join Date: 2002-10-25 Member: 1601Members
    OH GOD IT'S MATH RUN FOR YOUR LIVES!
  • ZiGGYZiGGY Join Date: 2003-01-19 Member: 12479Members
    .9 recurring infinite decimal is 1, it is by definition and it is by reason a part of infinite decimal systems, dont argue it any other way they are the same.
  • [WHO]Them[WHO]Them You can call me Dave Join Date: 2002-12-11 Member: 10593Members, Constellation
    <!--QuoteBegin-ZiGGY^+Jun 19 2004, 08:02 PM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (ZiGGY^ @ Jun 19 2004, 08:02 PM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> .9 recurring infinite decimal is 1, it is by definition <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
    Got a link?
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