To describe quantities that come up in basic geometry, such as \(\pi \) or \(\sqrt{2}\) , we need to move beyond \(\mathbb {Q}\) and allow for irrational numbers. The term real number was coined by René Descartes in the 17th century to distinguish the true roots of a polynomial from imaginary roots such as \(\sqrt{-1}\) . The real numbers were assumed to include all rational and irrational values. The development of calculus relied on some intuitive assumptions for the real number system, which could not be formulated precisely because there was no systematic definition of a real number.