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Improperly Convergent Sequence

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analysis

Definition

Uneigentlich Konvergente Folge

Improperly Convergent Sequence

A sequence whose elements become arbitrarily large with:

and can be denoted as as:

Analogously, one defines , and such sequence are also called improperly convergent. The values are then referred to as improper limits.

Examples

We assume that . Let be given. Find a such that for all we have .

Trivially, we can find a such that for all . However, this can be proven easily:

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