Here's another way to put it...

1 - .999... = 0.000...

Since there are an infinite amount of zeros, due to the mechanics of subtracting

(see: 1-.09 = .01, 1 -.009 = .001)

there is no valid way to express an infinite amount of zeros between the . and the 1, at least not in the conventional math that is used even in calculus (there may very well be theoretical methods for expressing this.) Because there will always be one more required step to solve the equation (1 more zero in the chain), the number repeats, infinitely. This logic does not mesh with our current understanding of reality, that is, that there are "building blocks" of the "building blocks" of protons, neutrons, and electrons. These are the smallest pieces of existence, and nothing can hold a smaller value than these things other than a concept referred to as "0", nothingness.

However, since the limit of x approaching 1 gets close to 1, yet never actually touches it, we wind up with what seems like a logical paradox. However, there must be a threshold - when does something become small enough to be zero? The answer would be, for our current understanding of the world, when something would be smaller than the smallest pieces of existence, we must either redefine the lower border of existence as we know it, or submit that it is no longer a part of existence, it is no longer something, it is nothing, it has a value of zero. This would also be exhibited in numbers, something infinitely small enough would be zero.

This leads us back to the number shown as 1-.999...

Since the result would be infinitely small, using the conclusion from the previous paragraph, 1-.999... = 0.

I should probably go back to work.

Should.