\begin{definition}[Definition:Cosine/Real Function]
The real function $\cos: \R \to \R$ is defined as:
{{begin-eqn}}
{{eqn | l = \cos x
      | r = \sum_{n \mathop = 0}^\infty \paren {-1}^n \frac {x^{2 n} } {\paren {2 n!} }
      | c = 
}}
{{eqn | r = 1 - \frac {x^2} {2!} + \frac {x^4} {4!} - \frac {x^6} {6!} + \cdots + \paren {-1}^n \frac {x^{2 n} } {\paren {2 n}!} + \cdots
      | c = 
}}
{{end-eqn}}
\end{definition}