Welcome, Goddess.

Well, I guess that is the thing about mathematics. It's gotta work all the time!

I suppose you read our page on 9 Recurring

Well, let us try with your variation: Does 1 + 0.999... = 2 ?

Let X = 0.999...
   
So, we are asking: Does 1+X = 2 ??

Let's start with: 1+X = 1.999...

Multiply by 10:  10(1+X) = 10(1.999...)
Or: 10+10X = 19.999...

Subtract X from each side to give us: 10 + 9X = 19.999... - X

but we know that X is 0.999..., so: 10 + 9X = 19.999... - 0.999...
or: 10 + 9X = 19
or: 9X = 19-10 = 9
or: X = 9/9 = 1 

So, X is equal to 1 and also equal to 0.999... (because we said so at the top)

Therefore 0.999... = 1