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What are Transcendal Numbers?

  1. Feb 15, 2006 #1
    Can someone please explain what are Transcendal Numbers are?
    and why they are so important?
  2. jcsd
  3. Feb 15, 2006 #2


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    A transcendental number is a number which isn't a root of any polynomial with integer coefficients. It's therefore not an algebraic number (of any degree).

    All transcendental numbers are irrational but the converse is not true. For example, [itex]\sqrt 2[/itex] is irrational but is a solution of [itex]x^2 = 2[/itex].
  4. Feb 15, 2006 #3


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    They are important in that almost all real numbers are transcendental.
  5. Feb 15, 2006 #4
    That means it should include e and Pi ?
    I read one time that e and pi are belived to be a root of some kind of an equation.
  6. Feb 15, 2006 #5


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    e and pi are both transcendental.
  7. Feb 15, 2006 #6

    matt grime

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    e and pi certainly are the roots of 'some kinds of equation', just not any polynomial over Q. They are roots if [itex]x^2-(e+\pi)x+e\pi[/itex], for instance.
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