Sequential Characterization of Limit at Positive Infinity of Real Function/Corollary

Corollary
Let $f : \R \to \R$ be a real function.

Let $L$ be a real number.

Then:
 * $\ds \lim_{x \to \infty} \map f x = L$




 * for all increasing real sequences $\sequence {x_n}_{n \mathop \in \N}$ with $x_n \to \infty$ we have $\map f {x_n} \to L$.