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Mind=Blown
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this post was submitted on 17 Jul 2023
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You are correct and I am wrong, I always assumed it to mean the same thing as a limit going to infinity that goes to 0
It's a weird concept and it's possible that I'm using it incorrectly, too - but the context at least is correct. :)
Edit: I think I am using it incorrectly, actually, as in reality the difference is infinitesimally small. But the general idea I was trying to get across is that there is no real number between 0.999... and 1. :)
I think you did use it right tho. It is a infinitesimal difference between 0.999 and 1.
"Infinitesimal" means immeasurably or incalculably small, or taking on values arbitrarily close to but greater than zero.
The difference between 0.999... and 1 is 0.
It is possible to define a number system in which there are numbers infinitesimally less than 1, i.e. they are greater than every real number less than 1 (but are not equal to 1). But this has nothing to do with the standard definition of the expression "0.999...," which is defined as the limit of the sequence (0, 0.9, 0.99, 0.999, ...) and hence exactly equal to 1.