Note that any function ℤ → ℝ is continuous on its domain but nowhere differentiable. A Scott-continuous function ℤ → ℝ must be monontonous. So not every such f

Note that any function ℤ → ℝ is continuous on its domain but nowhere differentiable. A Scott-continuous function ℤ → ℝ must be monontonous. So not every such function is Scott-continuous.