section_path: History/Transcendental numbers and reals
section_name: Transcendental numbers and reals
paragraph_text: Transcendental numbers and reals
  
  The existence of transcendental numbers was first established by Liouville (1844, 1851). Hermite proved in 1873 that e is transcendental and Lindemann proved in 1882 that π is transcendental. Finally, Cantor showed that the set of all real numbers is uncountably infinite but the set of all algebraic numbers is countably infinite, so there is an uncountably infinite number of transcendental numbers.