Does the Order Limit Theorem apply when aₙ ≤ bₙ?

[jdinatale]

Homework Statement

Limits, if they exist, must be unique

Homework Equations

Order Limit Theorem:

Assume $\lim a_n = a$ and $\lim b_n = b$.

(ii) If $a_n \leq b_n$, for all $n \in \mathbf{N}$, then $a \leq b$

The Attempt at a Solution

 

[Dick]

Looks fine to me.