 There is a common misunderstanding that constructive mathematics is just mathematics without proofs by contradiction (reductio-ad-absurdum arguments). This is not the case. Consider typical proofs that \(\sqrt{2}\) is irrational: these start with the assumption '\(\sqrt{2}\) is rational', then proceed by elementary, and fully constructive, steps to arrive at a contradiction. Such a procedure is a perfectly constructive proof that \(\sqrt{2}\) is not rational; indeed, the constructive interpretation of '\(\neg p\)' is precisely that assuming \(p\) leads to a contradiction. The misunderstanding alluded to at this start of this paragraph is caused by confusing a proof, like the foregoing, of a negated statement with one of the following type: assume \(\neg p\), derive a contradiction, and conclude that \(p\) must hold. From a constructive point of view, the most one can obtain from the latter type of proof is the conclusion \(\neg\neg p\); the final step, claiming that \(p\) must hold, is nonconstructive.