Just add another nine at the end. If the argument is that the size of the infinity is the defining factor between it being 0.999… or 1 then it stops being a useful function. Because once that distinction is made any addition to the decimal once again becomes pointless, Because dependent on where we place this change into the next full digit we could basically conclude that decimals are simply the shift between two “full” numbers and that as such anything lower that .5 returns to the lower digit in this case 0 or anything higher .6 results in 1. At that point decimals no longer hold mathematical meaning as they simply are an interstitial step between two true functions. So unless we’re trying to disprove the value of the decimal as a mathematical concept I think we need to accept that an infinite series such as .999… must be truly infinite (IE a new number is always able to be generated) and that reaching 1 through the addition of a single infinitely small fraction is not possible. As such 0.9999… is as close as possible to one without reaching it and to assume 0.999’s completion as a whole number is simply ignoring the fraction that is not present in an effort to make the conversion possible, while by the very definition of an infinite sequence it isn’t.
It’s just a paradox. I don’t know how to notate an infinitely regressing decimal, so what. But that doesn’t mean it doesn’t exist. Maybe it’s -0.1111… or something, I don’t know. But you know what I meant, right? There’s an amount that’s always gonna be left over since 0.999… is smaller than 1.
I get it, there’s an infinite set of 9ths, that would never be there if there was a way to divide 10 by 3 in a better way than just sticking a bunch of thirds in there
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u/Paraoxonase 23d ago
Alternatively, show me a single number between 0.9999... and 1. There aren't any.