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Glite Dictionary
transcendental number

transcendental number

1 9.9
A number that is not a solution of any polynomial equation with rational coefficients
  • noun
  • /ˌtræn.sɛnˈdɛn.təl ˈnʌm.bər/
  • Specialized
translation icon : número trascendental
  • Many mathematicians study transcendental numbers because they have unique properties compared to algebraic numbers.

Examples

  • Pi is a famous example of a transcendental number that cannot be expressed as a fraction.

  • A transcendental number cannot be expressed as a solution to a polynomial equation.

  • No algebraic equation with rational coefficients has a transcendental number as its solution.

  • Proving that e is a transcendental number was a major achievement in mathematics.

  • The number π is a famous example of a transcendental number.

  • Many mathematicians study transcendental numbers for their unique properties.

  • The existence of transcendental numbers was proven by Joseph Fourier, highlighting their importance in mathematics.

Antonyms

algebraic number
  • Specialized
9.5

A number that solves a polynomial equation with rational coefficients

Surface Forms

transcendental number singular
transcendental numbers plural

Morphology

transcendental + number

The phrase combines 'transcendental' (beyond ordinary) and 'number', so a learner might infer it denotes a special or non-ordinary kind of number, giving a partial clue. However the precise mathematical sense (not being a root of any nonzero polynomial with rational coefficients) is technical and not predictable from the constituents alone, so a B1 learner who knows the words would not derive the full meaning without prior exposure.

Etymology

Transcendental number comes from the word transcend, which means 'to go beyond', and the word number. It was named this because these numbers 'go beyond' ordinary algebra, so no algebra equation can have them as an answer.