what is the meaning of this sequence function $f_n=\mathbb 1_{[n, \infty)}?$

Question

what is the meaning of this sequence of functions $f_n=\mathbb 1_{[n, \infty)}?$

Actually after reading this solution, I got confused and didn't understand the given answer

Answer 1

For a subset $S$ of some domain $X$, $\mathbf{1}_S$ usually denotes the indicator function of $S$, i.e., the function $$ \mathbf{1}_S\colon X \to \{0,1\} $$ such that $\mathbf{1}_S(x)=1$ if $x\in S$, and $0$ otherwise.

In your case, the sets considered are intervals of the form $[n,\infty)$: so, for any integer $n$, $f_n$ is the function that takes value $0$ on $(-\infty, n)$ and $1$ on $[n,\infty)$.