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  2. Irrational number - Wikipedia

    en.wikipedia.org/wiki/Irrational_number

    However, there is a second definition of an irrational number used in constructive mathematics, that a real number is an irrational number if it is apart from every rational number, or equivalently, if the distance | | between and every rational number is positive. This definition is stronger than the traditional definition of an irrational number.

  3. Proof of impossibility - Wikipedia

    en.wikipedia.org/wiki/Proof_of_impossibility

    All of these are problems in Euclidean construction, and Euclidean constructions can be done only if they involve only Euclidean numbers (by definition of the latter). [9] Irrational numbers can be Euclidean. A good example is the square root of 2 (an irrational number).

  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. Arithmetic - Wikipedia

    en.wikipedia.org/wiki/Arithmetic

    For example, if a right triangle has legs of the length 1 then the length of its hypotenuse is given by the irrational number . π is another irrational number and describes the ratio of a circle's circumference to its diameter. [22] The decimal representation of an irrational number is infinite without repeating decimals. [23]

  6. Field (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Field_(mathematics)

    For example, any irrational number x, such as x = √ 2, is a "gap" in the rationals Q in the sense that it is a real number that can be approximated arbitrarily closely by rational numbers p/q, in the sense that distance of x and p/q given by the absolute value | x − p/q | is as small as desired. The following table lists some examples of ...

  7. Transcendental number - Wikipedia

    en.wikipedia.org/wiki/Transcendental_number

    For example, the square root of 2 is an irrational number, but it is not a transcendental number as it is a root of the polynomial equation x 2 − 2 = 0. The golden ratio (denoted φ {\displaystyle \varphi } or ϕ {\displaystyle \phi } ) is another irrational number that is not transcendental, as it is a root of the polynomial equation x 2 − ...

  8. 10 Hard Math Problems That Even the Smartest People in the ...

    www.aol.com/10-hard-math-problems-even-150000090...

    The Kissing Number Problem. A broad category of problems in math are called the Sphere Packing Problems. They range from pure math to practical applications, generally putting math terminology to ...

  9. Tetration - Wikipedia

    en.wikipedia.org/wiki/Tetration

    Other than the problems with the extensions of tetration, there are several open questions concerning tetration, particularly when concerning the relations between number systems such as integers and irrational numbers:

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