Proof: 0.999... Is Equal To 1

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  • Added: 21-May-07

0,99999... equals 1. How to prove 0,999... = 1. Amazingly simple and very interesting!

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Proof: 0.999... Is Equal To 1

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  • How about this....

    Since:

    1
    3 * --- = 1 and 3 * 0.3' = 0.9'
    3

    And because:


    1
    --- = 0.3' ;
    3


    Then:


    1 = 0.9'



    Read this link:
    http://en.wikipedia.org/wiki/0.999

    By angelseph 1167712936 Reply Spam [+1] Moderate Up Moderate Down
  • not equal

    this would only be thougth like in calculus when a limit get infinitely close to1 but it never becomes 1, we can only asume that 1 is a limit which can't be equal to .99999999

    By us0008 1165904754 Reply Spam [+1] Moderate Up Moderate Down
    • Yes, it is.

      What is the biggest number in the interval [0,1)?

      It's not .9999999... b/c that equals 1.

      There is no biggest number in that interval btw.

      By GA Boy 1192124170 Reply Spam [-1] Moderate Up Moderate Down
  • infinity zeros??

    lol
    like i mentioned...
    u assume there are infinite number of 9's...
    but when 10 x 0.9999.., the assumption doesn't stand anymore....
    true that 0.000...1(or 0.000...9 in this case) is neglible as it is too small...
    but no doubt it is still there

    By mountainpig 1165026626 Reply Spam [+1] Moderate Up Moderate Down
    • REPEATING F*CKING BAR!!!

      Did you make it through algebra??? Or even simple mathematics? I'm guessing not!

      There is no f*cking assumption made! IT is a given fact that a repeating bar over the nine implies that the nines continue on forever.

      Go back to grade school, moron.

      By GA Boy 1192124283 Reply Spam [-1] Moderate Up Moderate Down
  • I'm sorry...

    to disappoint you, but there is no last digit!! So it cannot be 0 at the end...there's just infinity of nines.

    By learnmore 1165016176 Reply Spam [+1] Moderate Up Moderate Down
  • the equation is wrong...

    there is one assumption made that is being neglected
    x=0.9999...
    but 10x=9.999...(but eventually the last digit is a zero)

    so for example
    x=0.99999
    10x=9.99990
    10x-x=9x=8.99991
    x=0.99999

    how bout that now
    proof me wrong???

    By mountainpig 1164978270 Reply Spam [+1] Moderate Up Moderate Down
    • Repeating Bar

      A repeating bar means that the nines continue forever.

      (0.99999999999...) means that the nines never stop.

      So, your agument is mute.

      By GA Boy 1192124006 Reply Spam [-1] Moderate Up Moderate Down
  • EndGame

    "infinity" is a concept, NOT a number. It is a concept that means
    "limitlessness." As such, it cannot be used with any mathematical
    operators. The symbols of , -, x, and / are arithmetic operators, and
    we can only use them for numbers.

    By bmw06 1196132215 Reply Spam Moderate Up Moderate Down
  • such a stupid mistake

    x=.999999(infinity)
    9x=9

    By MistPerson 1192152176 Reply Spam Moderate Up Moderate Down
  • Meet up with other people like you at MI

    By barbehugewomanva 1191484052 Reply Spam Moderate Up Moderate Down
  • a logical error

    you can't use .9> as x, because .9> is not a number, it is a representation of .9999 to the infinity. This is like saying x=y, which means any given value of x is what y is. In this case, the given value of x is .99999 and you claim it is equal to y which is 1. Logically, you can't substitute x with a value like .9>

    Now if you try to use a finite number of 9s instead of .9> you will not get the same answer. However in terms of calculus and limits, the above statement is already true by default, the limit of .9> as > approaches infinity, is 1. which means in terms of how many digits we are counting, .9> is like saying 1.

    So to whoever made this, sorry but you're just an idiot.

    By MistPerson 1166586780 Reply Spam [-1] Moderate Up Moderate Down
    • No, you're the idiot.

      And you made no sense. Go back to calculus b/c you need to learn some things.

      .9> does NOT represent .9999 "to the infinity." That would be an indeterminate power. Anything raised to infinity does not mean anything at all, ever.

      By GA Boy 1192124612 Reply Spam [-1] Moderate Up Moderate Down
    • Ok, let me clarify.

      .9> because I can't type the other symbol, i dunno how. So let's say I use .9> as the infinity symbol.

      You say I don't know calculus but yet you don't know that in calc, a number that infinitly head towards a number such as .9> to 1, can be treated as 1.

      Enough of that, but this is really just an algebra mistake. I will explain.

      Where you say 10x-x =9.9> - .9> = 9x is wrong. Simple really, multiply x with 9 like this 9*(.99999) gives you something with 8 point something, and 9.9>-.9> is 9, so thus 9 does not equal to 9x, hence this calculation is false.

      By MistPerson 1192151685 Reply Spam Moderate Up Moderate Down
    • Yeah, but simplify...

      and you get 1 again. You can multiply whatever you want to both sides. It equals the same when simplified.

      Let me ask you this: Does .33333333... = 1/3?

      By GA Boy 1192165328 Reply Spam Moderate Up Moderate Down
    • NO

      you are trying to define a base 3 number with a base 10 number and that is not possible because in order to convert you would have to add an infinitely small number and that is not possible, but for you to assume that because you cannot add it you are not supposed to is stupid on your part.

      By bmw06 1196132530 Reply Spam Moderate Up Moderate Down
    • do you mean round off?

      i can give you an opinion as an answer.

      .3> and 1/3 are technically for human purposes equal, but numerically, they are only representations of eachother, not equals.

      You said you can multiply whatever you want on both sides and it becomes the same, it's not true, simplifying, or rounding off does not count, because you can technically say by rounding off, that 1.9 is equal to 2.

      just out of my curiosity, what is your level of math?

      By MistPerson 1192168442 Reply Spam Moderate Up Moderate Down
    • Okay, I completely just misspelled

      ... "mathematicians."

      My bad.

      By GA Boy 1192208638 Reply Spam Moderate Up Moderate Down
  • Makes you wonder...

    do you still trust maths? :)

    By dotsi 1164286263 Reply Spam [-1] Moderate Up Moderate Down
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