the set of all real transcendental numbers is uncountable
Proof.
Denote and be the set of real transcendental and real algebraic numbers respectively. Suppose is countable
. Then the union is also countable, since is also countable, which is a contradiction
. Therefore must be uncountable.
Title | the set of all real transcendental numbers is uncountable |
---|---|
Canonical name | TheSetOfAllRealTranscendentalNumbersIsUncountable |
Date of creation | 2013-03-22 16:08:05 |
Last modified on | 2013-03-22 16:08:05 |
Owner | gilbert_51126 (14238) |
Last modified by | gilbert_51126 (14238) |
Numerical id | 11 |
Author | gilbert_51126 (14238) |
Entry type | Theorem |
Classification | msc 03E10 |