Let $S$ denote the set of sequences $a=\left(a_{1}, a_{2}, \ldots\right)$ of real numbers such that $a_{k}$ equals 0 or 1 for each $k$. Then the function $f: S \rightarrow \mathbb{R}$ defined by
\[
f\left(\left(a_{1}, a_{2}, \ldots\right)\right)=\frac{a_{1}}{10}+\frac{a_{2}}{10^{2}}+\ldots
\]
is
- injective but not surjective
- surjective but not injective
- bijective
- neither injective nor surjective
