>>16812963
OP is correct. Lets us start by asserting a pretty sensible construction with an infinitesimal.
[math]1 - ε = 0.999...[/math]
Now for all r where r is a real number, we know this holds true for infinitesimals:
[math]0 < ε < r[/math]

Now given the equation:
[math]X - Y = X[/math]
We are left with an ambiguity when solving for Y. It may be 0, or it may be an infinitesimal, IFF
[math]0.999... = 1[/math]

However we can preserve algebra if we instead allot for:
[math]1 = 0.999... + ε[/math]

Feel free to refute me.