Editing Number (section)

===Transcendental numbers and reals {{anchor|History of transcendental numbers and reals}}===
{{further|History of π}}

The existence of [[transcendental numbers]]<ref>{{cite web |last=Bogomolny |first=A. |author-link=Cut-the-Knot |title=What's a number? |work=Interactive Mathematics Miscellany and Puzzles |url=http://www.cut-the-knot.org/do_you_know/numbers.shtml |access-date=11 July 2010 |archive-url=https://web.archive.org/web/20100923231547/http://www.cut-the-knot.org/do_you_know/numbers.shtml |archive-date=23 September 2010 |url-status=live }}</ref> was first established by [[Joseph Liouville|Liouville]] (1844, 1851). [[Charles Hermite|Hermite]] proved in 1873 that ''e'' is transcendental and [[Ferdinand von Lindemann|Lindemann]] proved in 1882 that π is transcendental. Finally, [[Cantor's first uncountability proof|Cantor]] showed that the set of all [[real number]]s is [[uncountable|uncountably infinite]] but the set of all [[algebraic number]]s is [[countable|countably infinite]], so there is an uncountably infinite number of transcendental numbers.