You cannot use it as something that implies time which has nothing to do with a specific quantity, static, irrelevant of time. Unless you have an actual way of calculating what you want. I can very well accept that, as long as you use a logic that is correct. Saying that 0.(3) + 0.(1) = 0.(4) because *all* digits are 1+3=4, that I can accept. Won't be my preferred expression, but still it make sense for me. Saying though that you do something forever, or there is a shift of infinite digits etc etc should not make sense by definition of infinity.
why is 0.000...0009 = 0?Problem is, 0.000....0009 = 0 ;-)
I'm guessing you'd like to say that 1 - 0.000....0009 = 0.999..., which, is true, but, so is this:
0.999... + 0.999... = 1.999...
1.999... - 0.999... = 1
What I like to say is that all this lacks some definition, which more or less is an infinitesimal which is non-zero. Then we can define better decimals with infinite digits as a whole and have no paradoxes.
If we use infinitesimal I would claim that automatically by definition you have some error in your measurement, since you claim that you have a quantity that you cannot distinguish from 0. Then we can define two equalities. One that is absolute and one with having an error a quantity that is an infinitesimal.
Then we can think how we can actually distinguish two quantities of having or not an error. The same logic quantum physics use. There is no real sense declaring something as the "exactly X" if you have no way of measuring exactly anything. It is like asking a blind to speak about colors.
So I would personally conclude that equality has an error, always, if you use infinitesimals. So saying that 0.000...000999... is equal to zero or it -> 0 is the same thing.