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by peterhalburt33 1513 days ago
You can compute it digit by digit:

.999…/2 = .45 + .045 + .0045 + …
1 comments
jonsen 1513 days ago
Yes, but your argument goes circular with this. And someone could argue that

  .999.../2 = .499...  <=>  .999... = 2*.499... = .499...+.499...
which "surely must" have 8 as the rightmost digit. Moving it further away from 1.
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peterhalburt33 1513 days ago
Agreed this isn’t airtight, but if you accept the premise that real numbers are specified by their sequence decimal digits: .499…+.499… has 9 as its first digit after the decimal, 9 as its second and so on - the only other number that has this decimal expansion is .999… infinitely repeating, so these must be the same numbers.
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