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Why 0.9999… Equals 1

February 4th, 2017 by Math Tricks | Filed under Math Tricks.






Here is an illustration as to why 0.9999 (dot, dot, dot . . . ) is equal to one:

Do you see a problem with this “proof”?

 

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3 Responses to “Why 0.9999… Equals 1”

  1. Kerry | 4/02/17

    There’s no issue with this proof. It’s simply a matter of accepting the mathematical laws of equality and inequality.

    If not, the discussion is over.

    I find most have issue with this because of confusion between infinity and an infinite number of things.

  2. Spenser | 28/06/17

    Not all infinity’s are the same. 0.999… has an infinite number of 9’s after the decimal whereas 10 X 0.999… has an infinite – 1 number of 9’s after the decimal. both are infinities, but are different. If you could ever reach infinity (which you can’t) then when you do the following step:
    10x – x = 9.999… – 0.999…
    simplifying it would look like this
    9x-8.999…991
    which would again make x = 0.9999…

  3. Spenser | 28/06/17

    sorry, typo, should be: 9x=8.999…991 and not 9x-8.999…991

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