 There exist weak counterexamples to many classically valid statements. The construction of these weak counterexamples often follow the same pattern as the example above. For example, the argument that shows that the intermediate value theorem is not intuitionistically valid runs as follows. Let \(r\) be a real number in [−1,1] for which \((r\leq 0 \vee 0 \lt r)\) has not been decided, as in the example above. Define the uniformly continuous function \(f\) on \([0,3]\) by