Category:Convergent Real Sequences

This category contains results about Convergent Real Sequences.
Definitions specific to this category can be found in Definitions/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 $x$.