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	odds ratio ODETypesReductibleToTheVariablesSeparableCase ODE types reductible to the variables separable case ODETypesSolvableByTwoQuadratures ODE types solvable by two quadratures OffdiagonalEntry off-diagonal entry OkaCoherenceTheorem Oka coherence theorem OlgaLadyzhenskaya Olga Ladyzhenskaya OlgaOleinik Olga Oleinik OligomorphicPermutationGroup oligomorphic permutation group omegalimitSet omega limit set OmegaLimitSet1 Omegaspectrum Omega-spectrum OmegastabilityTheorem Ominimality o-minimality OneHundredSixtythree one hundred sixty-three