If $\lim_{n \to \infty} a_n= \infty $ then there is a $n_0 \in \mathbb N $ such that $ \forall n \ge n_0, a_{n+1} \ge a_n $ [duplicate]

If $$\lim_{n \to \infty} a_n= \infty $$ then there is a $n_0 \in \mathbb N $ such that $ \forall n \ge n_0$$$a_{n+1} \ge a_n .$$

Is that true? It seems true for me but I couldn't prove it or find an counter example.

I tried like this:

If $\forall n\in \mathbb N , \exists k_n \in \mathbb N : a_{k_{n+1}} < a_{k_n} $

I tried to find any contradiction with that but I faild. So I want to know if my assumption is true or not?