In Foundations of Mathematics, it states that
"If $x$ and $y$ are different numbers on the line and we wish to distinguish between them, all we need do is find $n$ such that $1/10^n$ is less than their difference: then their expansion to $n$ places will differ."
Wouldn't a more accurate statement be "is less than or equal to their difference" ? For example, $0.08$ and $0.09$ differ by $1/10^2$ where $n = 2$, but $.01$ (the difference) is not less than $1/10^2$.