In standard analysis, it is a well-known result that $0.999...=1$, as $0.999...$ is defined to equal
$$\sum_{k=1}^\infty\frac9{10^k}=1.$$
However, in NSA limits are handled differently. I'm not well-versed in NSA, so I might be completely wrong, but that series should converge to $1-\varepsilon$, for some infinitesimal $\varepsilon$. Am I correct to say that, in NSA, $0.999...\approx1$ holds, but not $0.999...=1$?
