0.999... is as much an approximation to 1 as 0.333... is to 1/3. That is, not at...

		jhanschoo on April 27, 2022 \| parent \| context \| favorite \| on: Now I’m calculating with constructive reals 0.999... is as much an approximation to 1 as 0.333... is to 1/3. That is, not at all, since we use these representations to stand in for the rational number that is their limit. You will find that exactly the numbers that can be represented exactly in finite digits (a.k.a. ending in 000...) have two representations.

This holds for bases other than 10 as well. In base 3, 1/3 has two representations 0.1 and 0.0222...