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  2. Irrational number - Wikipedia

    en.wikipedia.org/wiki/Irrational_number

    An example of an irrational algebraic number is x 0 = (2 1/2 + 1) 1/3. It is clearly algebraic since it is the root of an integer polynomial, ) = ...

  3. List of types of numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_numbers

    Algebraic number: Any number that is the root of a non-zero polynomial with rational coefficients. Transcendental number: Any real or complex number that is not algebraic. Examples include e and π. Trigonometric number: Any number that is the sine or cosine of a rational multiple of π.

  4. Category:Irrational numbers - Wikipedia

    en.wikipedia.org/wiki/Category:Irrational_numbers

    In mathematics, an irrational number is any real number that is not a rational number, i.e., one that cannot be written as a fraction a / b with a and b integers and b not zero. This is also known as being incommensurable, or without common measure. The irrational numbers are precisely those numbers whose expansion in any given base (decimal ...

  5. Totally disconnected space - Wikipedia

    en.wikipedia.org/wiki/Totally_disconnected_space

    The following are examples of totally disconnected spaces: Discrete spaces; The rational numbers; The irrational numbers; The p-adic numbers; more generally, all profinite groups are totally disconnected. The Cantor set and the Cantor space; The Baire space; The Sorgenfrey line; Every Hausdorff space of small inductive dimension 0 is totally ...

  6. Repeating decimal - Wikipedia

    en.wikipedia.org/wiki/Repeating_decimal

    Any number that cannot be expressed as a ratio of two integers is said to be irrational. Their decimal representation neither terminates nor infinitely repeats, but extends forever without repetition (see § Every rational number is either a terminating or repeating decimal). Examples of such irrational numbers are √ 2 and π. [3]

  7. Algebraic number - Wikipedia

    en.wikipedia.org/wiki/Algebraic_number

    For example, all rational numbers have degree 1, and an algebraic number of degree 2 is a quadratic irrational. The algebraic numbers are dense in the reals . This follows from the fact they contain the rational numbers, which are dense in the reals themselves.

  8. Irrationality measure - Wikipedia

    en.wikipedia.org/wiki/Irrationality_measure

    Rational numbers have irrationality exponent 1, while (as a consequence of Dirichlet's approximation theorem) every irrational number has irrationality exponent at least 2. On the other hand, an application of Borel-Cantelli lemma shows that almost all numbers, including all algebraic irrational numbers , have an irrationality exponent exactly ...

  9. Number - Wikipedia

    en.wikipedia.org/wiki/Number

    In mathematics, the notion of number has been extended over the centuries to include zero (0), [3] negative numbers, [4] rational numbers such as one half (), real numbers such as the square root of 2 and π, [5] and complex numbers [6] which extend the real numbers with a square root of −1 (and its combinations with real numbers by adding or ...