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yetAnotherUser@discuss.tchncs.de ⁨5⁩ ⁨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 is equal to -1:

...999 = x
...990 = 10x

Calculate x - 10x:

x - 10x = ...999 - ...990
-9x = 9
x = -1

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

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