Anyway, in the surreal numbers you could probably make up a notation where 0.999... actually denotes 1 - ε or something. But I daresay it might not be very useful because then how do you denote 1 - ε/2 or anything else.
I don't know whether repeating decimals are useful for testing equality of surreal numbers.
All I'm trying to say is we're all talking about anything and everything except the definition "when are two real numbers equal?"
And then we're saying people who don't understand the consequences of that definition are kind of dummies ... while we continue to not actually say what the definition is.
1.000...0 = 1
1.000...05 = 1 + ε/2
1.000...1 = 1 + ε
0.999...8 = 1 - 2ε
0.999...9 = 1 - ε
0.999...98 = 1 - ε/5
.
.
.> 0.999...98 = 1 - ε/5
cough