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    Wikipedia
    https://en.wikipedia.org/wiki/Transcendental_number

    Transcendental number - Wikipedia

    In mathematics, a transcendental number is a real or complex number that is not algebraic – that is, not the root of a non-zero polynomial of finite degree with rational coefficients. The best-known transcendental numbers are π and e. Though only a few classes of transcendental numbers are known – partly because it … Visa mer

    History

    The name "transcendental" comes from Latin trānscendere 'to climb over or beyond, surmount', and was first used for the mathematical … Visa mer

    Numbers proven to be transcendental

    Numbers proven to be transcendental:
    • e if a is algebraic and nonzero (by the Lindemann–Weierstrass theorem).
    • π (by the Lindemann–Weierstrass theorem Visa mer

    Proofs for specific numbers

    A proof that e is transcendental
    The first proof that the base of the natural logarithms, e, is transcendental dates from 1873. We will now follow the strategy of David Hilbert Visa mer

    External links

    • Weisstein, Eric W. "Transcendental Number". MathWorld.
    • Weisstein, Eric W. "Liouville Number". MathWorld. Visa mer

    Properties

    A transcendental number is a (possibly complex) number that is not the root of any integer polynomial. Every real transcendental number must also be irrational, … Visa mer

    Possible transcendental numbers

    Numbers which have yet to be proven to be either transcendental or algebraic:
    • Most sums, products, powers, etc. of the number π and the number e, e.g. eπ, e + π, π − e, π/e, π , e , … Visa mer

    Sources

    • Adamczewski, Boris; Bugeaud, Yann (2005). "On the complexity of algebraic numbers, II. Continued fractions". Acta Mathematica. … Visa mer

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  2. Wikipedia
    https://sv.wikipedia.org/wiki/Transcendenta_tal

    Transcendenta tal – Wikipedia

  4. Brilliant
    https://brilliant.org/wiki/transcedental-number

    Transcendental Numbers | Brilliant Math & Science Wiki

    Taggar:
    Transcendental Numbers
    Algebraic and Transcendental Number
  5. Britannica
    https://www.britannica.com/science/transcendental-number

    Transcendental number | Definition & Facts | Britannica

    Taggar:
    Transcendental Number Importance
    Transcendental Number Examples
    +3
    Algebraic Number
    All Transcendental Numbers
    Define Transcendental
  6. Andra har också frågat
    What is a transcendental number?
    Transcendence theory is concerned with the converse question: given a complex number , is there a polynomial with rational coefficients such that If no such polynomial exists then the number is called transcendental. More generally the theory deals with algebraic independence of numbers.

    Transcendental number theory - Wikipedia

    en.wikipedia.org
    Is a transcendental number irrational?
    A transcendental number is a (possibly complex) number that is not the root of any integer polynomial. Every real transcendental number must also be irrational, since a rational number is the root of an integer polynomial of degree one. The set of transcendental numbers is uncountably infinite.

    Transcendental number - Wikipedia

    en.wikipedia.org
    Why are transcendental numbers uncountable?
    Since the real numbers are the union of algebraic and transcendental numbers, it is impossible for both subsets to be countable. This makes the transcendental numbers uncountable. No rational number is transcendental and all real transcendental numbers are irrational.

    Transcendental number - Wikipedia

    en.wikipedia.org
    Who was the first person to define transcendental numbers?
    Euler, in the 18th century, was probably the first person to define transcendental numbers in the modern sense. Johann Heinrich Lambert conjectured that e and π were both transcendental numbers in his 1768 paper proving the number π is irrational, and proposed a tentative sketch proof that π is transcendental.

    Transcendental number - Wikipedia

    en.wikipedia.org
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  7. Wolfram MathWorld
    https://mathworld.wolfram.com/TranscendentalNumber.html

    Transcendental Number -- from Wolfram MathWorld

    Taggar:
    Algebraic Number
    Transcendental Number
  8. Math is Fun
    https://www.mathsisfun.com/numbers/transcendental-numbers.html

    Transcendental Numbers - Math is Fun

    Taggar:
    Algebraic and Transcendental Number
    Transcendental Number Examples
    +3
    Transcendental Number Importance
    List of Transcendental Numbers
    Transcendental Function
  9. Encyclopedia of Mathematics
    https://encyclopediaofmath.org/wiki/Transcendental_number

    Transcendental number - Encyclopedia of Mathematics

  10. Wikipedia
    https://en.wikipedia.org/wiki/Transcendentalnumber

    Wikipedia

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