• TechieDamien@lemmy.ml
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    1 year ago

    This is not a proof as you start with the answer, albeit disguised as a known truth. Here is a real proof. Start by assigning the recurring decimal a variable.

    x = 0.9999...
    

    Now calculate 10 times this by shifting the decimal place.

    10x = 9.9999...
    

    You can then subtract the second equation from the first. Note that all the digits after the decimal cancel out, leaving us with the following.

    9x = 9
    x = 1
    

    Therefore, 0.9999… = 1. Infinity does weird things!