Limit to Infinity of x minus Gamma of Reciprocal of x

Theorem

 * $\displaystyle \lim_{x \mathop \to \infty} \paren {x - \map \Gamma {\dfrac 1 x} } = \gamma$

where:
 * $\Gamma$ denotes the $\Gamma$ (Gamma) function
 * $\gamma$ denotes the Euler-Mascheroni constant.