u/AnotherOneElse

I almost iterally said there are there are infinite integers. You still don't get the point, silly.

If all of them are finite, then, no matter how much or how fast are you increazing n in 1-1/10^n, because n is still finite.

Unless you can find one integer n that is not finite, then 1-1/10^n is permanently less than 0.999...

The gap is never 0

0.999... - (1-1/10) = 0.0999...

0.999... - (1-1/10^2) = 0.00999...

0.999... - (1-1/10^3) = 0.000999...

The gap is never 0, brud.

Infinite sequences are limitless in elements, but not necessarily in value.

Taking the limit of the sequence refers to its value, not its amount of elements, and, if they value isn't limitless, then it's limitFULL, and limits do apply to the limitFULL, brud.

Saying something is A fact (grammar is important, brud) doesn't make it to be. You know that, right? Brud.

However, saying something is a fact, when there is a counterexample, that you are unable to even understand how is defined, is lying. So I will ask once again. Why do you keep lying? Brud.