\begin{definition}[Definition:Convergent Sequence/Real Numbers]
Let $\sequence {x_k}$ be a sequence in $\R$.
The sequence $\sequence {x_k}$ '''converges to the limit $l \in \R$''' {{iff}}:
:$\forall \epsilon \in \R_{>0}: \exists N \in \R_{>0}: n > N \implies \size {x_n - l} < \epsilon$
where $\size x$ denotes the absolute value of $x$.
\end{definition}