this post was submitted on 27 Jun 2024
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No, it equals 0.999...
2/9 = 0.222... 7/9 = 0.777...
0.222... + 0.777... = 0.999... 2/9 + 7/9 = 1
0.999... = 1
No, it equals 1.
Sure, when you start decoupling the numbers from their actual values. The only thing this proves is that the fraction-to-decimal conversion is inaccurate. Your floating points (and for that matter, our mathematical model) don't have enough precision to appropriately model what the value of 7/9 actually is. The variation is negligible though, and that's the core of this, is the variation off what it actually is is so small as to be insignificant and, really undefinable to us - but that doesn't actually matter in practice, so we just ignore it or convert it. But at the end of the day 0.999... does not equal 1. A number which is not 1 is not equal to 1. That would be absurd. We're just bad at converting fractions in our current mathematical understanding.
Edit: wow, this has proven HIGHLY unpopular, probably because it's apparently incorrect. See below for about a dozen people educating me on math I've never heard of. The "intuitive" explanation on the Wikipedia page for this makes zero sense to me largely because I don't understand how and why a repeating decimal can be considered a real number. But I'll leave that to the math nerds and shut my mouth on the subject.
You are just wrong.
The rigorous explanation for why 0.999...=1 is that 0.999... represents a geometric series of the form 9/10+9/10^2+... by definition, i.e. this is what that notation literally means. The sum of this series follows by taking the limit of the corresponding partial sums of this series (see here) which happens to evaluate to 1 in the particular case of 0.999... this step is by definition of a convergent infinite series.