T or F?
1) If $x_n \rightarrow 0$ and $x_n \neq 0$ for all $n$, then the sequence {$1/n$} is unbounded.
Also similarly...
2) If {$x_n$} is unbounded and $x_n \neq 0$ for all $n$, then $1/x_n \rightarrow 0$.
For the first one, I would say that is true because the limit of {$1/n$} would approach infinity, thus making it unbounded?
And the second one, also seems true by similar logic. Am I overlooking something here?