The sequence $x_n=2+1/n$ certainly gets "closer and closer" to $2$ as $n$ gets "larger and larger." And we know that $\lim_{n\to\infty}2+1/n=2$ What's going on here? Use the definition to explain what we really mean when we say a sequence gets "closer and closer" to the limit.
I'm not sure how to explain it with the definition..