transcendental number

A transcendental number is a complex numberthat is not an algebraic number.That is, it is a complex number that is transcendental over $\\mathbb{Q}$ (or, equivalently, over $\\mathbb{Z}$ ).

Well known transcendental numbers include $\\pi$ and $e$ (the base of natural logarithms).

Cantor showed that, in a sense,“almost all” complex numbers are transcendental:there are uncountably many complex numbers, butonly countably many algebraic numbers (http://planetmath.org/AlgebraicNumbersAreCountable).

单词	TranscendentalNumber
释义	transcendental number A transcendental number is a complex numberthat is not an algebraic number.That is, it is a complex number that is transcendental over $\\mathbb{Q}$ (or, equivalently, over $\\mathbb{Z}$ ). Well known transcendental numbers include $\\pi$ and $e$ (the base of natural logarithms). Cantor showed that, in a sense,“almost all” complex numbers are transcendental:there are uncountably many complex numbers, butonly countably many algebraic numbers (http://planetmath.org/AlgebraicNumbersAreCountable).
随便看	NagellLutzTheorem Nagell-Lutz theorem Naive van Kampen NakayamasLemma Nakayama’s lemma NapoleonsTheorem Napoleon’s theorem NashEquilibrium Nash equilibrium NashIsometricEmbeddingTheorem Nash isometric embedding theorem NationalScienceFoundation National Science Foundation NaturalBoundary natural boundary NaturalDeduction natural deduction NaturalDeductionForIntuitionisticPropositionalLogic natural deduction for intuitionistic propositional logic NaturalDeductionForPropositionalLogic natural deduction for propositional logic NaturalEquivalenceOfCGAndCMCategories natural equivalence of C_G and C_M categories NaturalHomomorphism natural homomorphism