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2. Rational number - Wikipedia

   en.wikipedia.org/wiki/Rational_number

   In mathematics, a rational number is a number that can be expressed as the quotient or fraction ⁠ ⁠ of two integers, a numerator p and a non-zero denominator q. [ 1] For example, ⁠ ⁠ is a rational number, as is every integer (e.g., ). The set of all rational numbers, also referred to as " the rationals ", [ 2] the field of rationals[ 3 ...

3. Irrational number - Wikipedia

   en.wikipedia.org/wiki/Irrational_number

   Irrational number. The number √ 2 is irrational. In mathematics, the irrational numbers ( in- + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, the line segments are also ...

4. Diophantine approximation - Wikipedia

   en.wikipedia.org/wiki/Diophantine_approximation

   In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria . The first problem was to know how well a real number can be approximated by rational numbers. For this problem, a rational number p / q is a "good" approximation of a real number ...

5. Algebraic number - Wikipedia

   en.wikipedia.org/wiki/Algebraic_number

   An algebraic number is a number that is a root of a non-zero polynomial (of finite degree) in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, , is an algebraic number, because it is a root of the polynomial x2 − x − 1. That is, it is a value for x for which the polynomial evaluates to zero.

6. List of types of numbers - Wikipedia

   en.wikipedia.org/wiki/List_of_types_of_numbers

   All rational numbers are real, but the converse is not true. Irrational numbers (): Real numbers that are not rational. Imaginary numbers: Numbers that equal the product of a real number and the imaginary unit , where =. The number 0 is both real and imaginary.

7. Hurwitz's theorem (number theory) - Wikipedia

   en.wikipedia.org/wiki/Hurwitz's_theorem_(number...

   In number theory, Hurwitz's theorem, named after Adolf Hurwitz, gives a bound on a Diophantine approximation. The theorem states that for every irrational number ξ there are infinitely many relatively prime integers m, n such that. The condition that ξ is irrational cannot be omitted. Moreover the constant is the best possible; if we replace ...