lvxferre, (edited )
@lvxferre@lemmy.ml avatar

Because it isn’t 0.9; it’s 0.999… with the ellipsis saying “repeat this to the infinite” being part of the number. And you don’t need to round it up to get 0.999… = 1, since the 9 keeps going on and on, so their difference is infinitesimally small = zero.

Another thing showing that they’re the same number is that there is no number between them. For example:

  • 0.9 (no ellipsis) and 1 are different because 0.95 is between them
  • 0.95 and 1 are different because 0.97 is between them
  • there’s no number between 0.999… (with ellipsis) and 1, so they are the same. inb4 no “last nine” because it’s infinite.
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