I have a confusion in my mind. Consider two sequences of real numbers $\{x_n\}$ and $\{y_n\}$. Define $z_n: = x_n -y_n$. Suppose $x_n, y_n$ are two diverging sequences.
Then what can be said about the limit of $z_n$?
Can I say that we can split this into two cases:
Case 1. $x_\infty = y_\infty = z_\infty = +\infty$
Case 2. $x_\infty = y_\infty = +\infty$ and $z_\infty$ is finite.
Is it? Please help.
