 The weak counterexamples, introduced by Brouwer in 1908, are the first examples that Brouwer used to show that the shift from a classical to an intuitionistic conception of mathematics is not without consequence for the mathematical truths that can be established according to these philosophies. They show that certain classical statements are presently unacceptable from an intuitionistic point of view. As an example, consider the sequence of real numbers given by the following definition: 