1 = 0.99999...

Tags:
Mathematics Numbers Arithmetic Writing Proof Explain Mystery Question
RO-angel
  • Submitter:
    RO-angel
  • Visits: 1,435
  • Subscribers: 1
  • Comments: 0
  • Updated: 24-Jul-07
  • Videos: 8
  • International International
  • Comments: 16
  • Views: 13,004
  • Added: 22-Jan-07

1 = 0.9999... ?

  1. Categories: Comedy
  2. Favorite On: raven_hell
Comments on

1 = 0.99999...

16 Comments | Add Comment
  • 1 != 0.9999...

    i've seen this video posted somewhere in metacafe before...
    n i've posted the flaw in that video, so might as well do it here

    the flaw is that u assumed that
    10 x 0.999...= 9.999...

    however the truth is that
    10 x 0.999 = 9.999....990(the last digit has to be a zero)

    hence,
    10x - x = 9.999...990 - 0.9999...
    9x = 8.999....991
    x = 0.999...

    anyway nice try on fooling with kids who aren't fundamentally strong at maths..

    By mountainpig 1174971257 Reply Spam [+2] Moderate Up Moderate Down
    • 10x = 9.999...990?

      As that may be, the number of 9's go on infinitely, which means 9.999(bar) is equal to 9.999...(infinite 9's)...990
      So either way this would be true :D

      By deviouslife 1199047409 Reply Spam Moderate Up Moderate Down
    • 1!=0,99..??? ...another great sage....

      "anyway nice try on fooling with kids who aren't fundamentally strong at maths.."That was quite a confident phrase from u even so u are wrong:) The bar on the 9 represents that its 0,99... (somewhere they use point in place of the bar), not 0,99..90. So it's an infinite sum, which is convergant and its sum is 1. So it's the same, but we use 1 and not 0,999 because: 1., it's simplier 2., usually in the structure of math we define the real numbers first and the infinite sums ust afterwards. So the video is true, but it can confuse the ones who aren't fundamentally strong at maths.. :)

      By huncros 1193662702 Reply Spam Moderate Up Moderate Down
    • 10 x 0.999 =9.99

      x = 0.999
      10x = 9.99
      10x - x = 9.99 - x
      9x=9.99 - x
      9x=8.991
      x=9/8.991
      x=0.999

      By nassim21 1191428256 Reply Spam Moderate Up Moderate Down
    • Excellent explanation

      I was watching this and was ready to post something similar, but you hit it right on the nose. Couldn't have said it better myself.

      By MrKowz 1185843412 Reply Spam Moderate Up Moderate Down
    • h

      0.999 with a bar at the top is 1

      By 61003 1185232795 Reply Spam [-1] Moderate Up Moderate Down
    • 0.999 (bar) != 1

      No, 0.999 with a bar on the top is not 1. It just comes very, very close.

      nassim21, stop posting your comment. You're wrong, x = 0.999 BARRED. This means that the number of 9's that come after the decimal point is infinite. This may be correct math, but it is not the numbers used in the video.

      By deviouslife 1199047236 Reply Spam Moderate Up Moderate Down
    • 1 # 0.999

      x = 0.999
      10x = 9.99
      10x - x = 9.99 - x
      9x=9.99 - x
      9x=8.991
      x=9/8.991
      x=0.999

      By nassim21 1191428293 Reply Spam Moderate Up Moderate Down
  • fuckin noobs

    what a bunch of fuckin noobs

    By MathPhDeeznutz 1214939232 Reply Spam Moderate Up Moderate Down
  • The proof is correct

    If you need another way to prove it, 'equals' can be defined as
    if abs(a-b)<m for all m>0 then a=b
    suppose you were to choose m = 10^-9, then simply carry the repeat out 10 times and concatenate (cuz rounding would actually be beneficial) and you'll still be fine.
    abs (1-.9999999999) = 10^-10
    10^-10 < 10^-9
    if you want an even tighter tollerance, go with m=10^-100. or m=10^-1000. or the limit as m approaches zero positively. No matter how small m is, you can always take .9bar out further such that 1-.9bar is less than your tollerance

    By keyboarder 1214126785 Reply Spam Moderate Up Moderate Down
  • this is true

    .999... is shorthand for the sum of an infinite series of decimals, which is defined in terms of a limit. anyone can see here that the limit of .999... is 1, since it keeps getting closer and closer to 1 as the decimals go further out. the only room for debate lies in how inadequate your understanding of mathematical notation is.

    .999999999... = 1, just like .333333... = 1/3 and 3824.555... = 3824 + 5/9. these are merely different representations of the same numbers.

    By boobajoob 1213072799 Reply Spam Moderate Up Moderate Down
  • 9x = 8,999(bar)

    I know shit about math. But this just can't be true.

    In my opinion, the distance between 9,999(bar) and 10 [at 10x=9,999(bar)] should get ten times infinitesimally bigger than the one between 0,999(bar) and 1 -as it does with rational numbers (0,98 it's 0,02 far from 1; 9,8 it's 0,2 from 10).

    Hence, in the example, the ",999(bar)" inside 9,999(bar) is infinitesimally smaller than X; forcing the result of subtracting X from 10x to be logically smaller than 9.

    9x=8,999(bar)

    x=8,999(bar)/9

    x=0,999(bar)

    By unopinionated 1207585999 Reply Spam Moderate Up Moderate Down
  • ... And if that was 2 easy...

    0,999... = 9/10 + 9/100 + ... + 9/10^n (where n approaches infinity)
    This series converges (geometrical series, where q=1/10)
    So the sum of this series is
    9 * [1/(1-1/10) - 1] = 9 * [10/9 - 1] = 9 * 1/9 = 1
    So, it's still one.

    By ozzyl 1191506140 Reply Spam Moderate Up Moderate Down
  • Another way

    (I like this better, at least it's smaller)
    0,999... = 3 x 0,333... = 3 x 1/3 = 1
    :P

    By ozzyl 1191506036 Reply Spam Moderate Up Moderate Down
  • ummm...

    999 / 1000 =.999. How can you be a stupid math nerd?

    By 7heBa6 1182469210 Reply Spam [-2] Moderate Up Moderate Down
16 Comments | Add Comment