 In what follows, we use bold \(\bR\) to distinguish the real line in SIA from its counterparts in classical and constructive analysis. In the usual development of the calculus, for any differentiable function \(f\) on the real line \(\bR, y = f(x)\), it follows from Taylor’s theorem that the increment \(\delta y = f(x + \delta x) - f(x)\) in \(y\) attendant upon an increment \(\delta x\) in \(x\) is determined by an equation of the form