Działania na granicach ciągów

Jeżeli $lim_{n \to \infty} a_{n} = a$ i $lim_{n \to \infty} b_{n} = b$ to:

$lim_{n \to \infty} (a_{n} + b_{n}) = a + b$ ,

$lim_{n \to \infty} (a_{n} - b_{n}) = a - b$ ,

$lim_{n \to \infty} (a_{n} b_{n}) = a b$ ,

$\underset{k \in N^{+}}{\exists} \underset{n > k}{\forall} (b_{n} \neq 0 \land b \neq 0) \Rightarrow lim_{n \to \infty} \frac{a_{n}}{b_{n}} = \frac{a}{b}$ ,

$\underset{k \in N^{+}}{\exists} \underset{n > k}{\forall} (a_{n} \geq b_{n} \Rightarrow a \geq b)$ .