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We consider Gomory and Johnson's infinite group model with a single row.Valid inequalities for this model are expressed by valid functions and it hasbeen recently shown that any valid function is dominated by some nonnegativevalid function, modulo the affine hull of the model. Within the set ofnonnegative valid functions, extreme functions are the ones that cannot beexpressed as convex combinations of two distinct valid functions. In this paperwe construct an extreme function $\pi:\mathbb{R} \to [0,1]$ whose graph isdense in $\mathbb{R} \times [0,1]$. Therefore, $\pi$ is discontinuouseverywhere.

An extreme function which is nonnegative and discontinuous everywhere