Khác biệt giữa bản sửa đổi của “Số vô tỉ”

[[Johann Heinrich Lambert|Lambert]] proved (1761) that π cannot be rational, and that ''e''^''n'' is irrational if ''n'' is rational (unless ''n'' = 0)<ref>{{chú thích tạp chí|title=Mémoire sur quelques propriétés remarquables des quantités transcendentes circulaires et logarithmiques|journal=Histoire de l'Académie Royale des Sciences et des Belles-Lettres der Berlin|author=J. H. Lambert|year=1761|pages=265-276}}</ref>. While Lambert's proof is often said to be incomplete, modern assessments support it as satisfactory, and in fact for its time unusually rigorous. [[Legendre]] (1794), after introducing the [[Bessel-Clifford function]], provided a proof to show that π² is irrational, whence it follows immediately that π is irrational also. The existence of transcendental numbers was first established by Liouville (1844, 1851). Later, Georg Cantor (1873) proved their existence by a different method, that showed that every interval in the reals contains transcendental numbers. [[Charles Hermite]] (1873) first proved <math>e</math> transcendental, and [[Ferdinand von Lindemann]] (1882), starting from Hermite's conclusions, showed the same for π. Lindemann's proof was much simplified by Weierstrass (1885), still further by [[David Hilbert]] (1893), and has finally been made elementary by [[Adolf Hurwitz]] andvà [[Paul Albert Gordan]].

== Tài liệu thamTham khảo ==