Let $f: \mathbb{R}\rightarrow\mathbb{R}$ be a continuous function and $A \subset \mathbb{R}$ be defined by
$A=\left\{ y \in \mathbb{R}:y = \displaystyle \lim_{n \rightarrow \infty} f(x_{n}), \text {for some sequence} x_{n} \rightarrow +\infty\right\}$
Then the set A is necessarily.
- $A$ connected set
- $A$ compact set
- $A$ singleton set
- None of the above
