# Category:Definitions/Convergent Real Sequences

This category contains definitions related to Convergent Real Sequences.
Related results can be found in Category:Convergent Real Sequences.

Let $\sequence {x_k}$ be a sequence in $\R$.

The sequence $\sequence {x_k}$ converges to the limit $l \in \R$ if and only if:

$\forall \epsilon \in \R_{>0}: \exists N \in \R_{>0}: n > N \implies \size {x_n - l} < \epsilon$

where $\size x$ denotes the absolute value of $x$.

## Pages in category "Definitions/Convergent Real Sequences"

The following 2 pages are in this category, out of 2 total.