• yetAnotherUser@discuss.tchncs.de
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    4 months ago

    Unfortunately not an ideal proof.

    It makes certain assumptions:

    1. That a number 0.999… exists and is well-defined
    2. That multiplication and subtraction for this number work as expected

    Similarly, I could prove that the number which consists of infinite 9’s to the left of the decimal separator is equal to -1:

    ...999.0 = x
    ...990.0 = 10x
    
    Calculate x - 10x:
    
    x - 10x = ...999.0 - ...990.0
    -9x = 9
    x = -1
    

    And while this is true for 10-adic numbers, it is certainly not true for the real numbers.