Let $X : \Omega : \rightarrow \mathbb{R}$ a random variable defined over some probability space $(\Omega, \mathcal{F}, \mathbb{P})$. The cumulative distribution function of $X$ is the function $F_X \colon \mathbb{R} \to [0, 1]$ where $F_X(x) = P(X \leq x)$.
I wanted to show that $\lim_{k \rightarrow \infty}F(k)=1$ where $k$ takes only integer
I would appreciate it if someone would get me started on this.