You will have to be more precise about what:

"f(x)-g(x)<<1"

(It seems likely that you mean "|f(x)-g(x)|<<1" that is the difference is close to zero, rather than "f(x)-g(x)" is of large absolute value and negative.)

and

" ~ "

means, what happens is that:

as and under one interpretation and under another

RonL