The set of continuous viscosity solutions of the infinity Laplace
equation $-\bigtriangleup^N_{\infty}w(x) = f(x)$ with generally
sign-changing right-hand-side $f$ in a bounded domain is analyzed.
The existence of a least and a greatest continuous viscosity
solutions up to the boundary is proved through a Perron's
construction by means of a strict comparison principle. These
extremal solutions are proved to be absolutely extremal solutions.