Improperly Convergent Sequence

analysis

Definition

Uneigentlich Konvergente Folge

Improperly Convergent Sequence

A sequence $(a_n{)}_{n\ge 0}$ whose elements become arbitrarily large with:

$$\forall K>0:\exists N(K)\in \mathbb{N}:\forall n>N(K):a_n>K$$

and can be denoted as as:

$$\underset{n\to \infty }{\lim }{a}_n=\infty$$

Analogously, one defines ${\lim }_{n\to \infty }{a}_n=-\infty$, and such sequence are also called improperly convergent. The values $+\infty ,-\infty$ are then referred to as improper limits.