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  2. List of types of numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_numbers

    Fractions: A representation of a non-integer as a ratio of two integers. These include improper fractions as well as mixed numbers. Continued fraction: An expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its ...

  3. Non-integer base of numeration - Wikipedia

    en.wikipedia.org/wiki/Non-integer_base_of_numeration

    The numbers d i are non-negative integers less than β. This is also known as a β-expansion, a notion introduced by Rényi (1957) and first studied in detail by Parry (1960). Every real number has at least one (possibly infinite) β-expansion. The set of all β-expansions that have a finite representation is a subset of the ring Z[β, β −1].

  4. Integer - Wikipedia

    en.wikipedia.org/wiki/Integer

    [12] [13] Only positive integers were considered, making the term synonymous with the natural numbers. The definition of integer expanded over time to include negative numbers as their usefulness was recognized. [14] For example Leonhard Euler in his 1765 Elements of Algebra defined integers to include both positive and negative numbers. [15]

  5. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    A simple fraction (also known as a common fraction or vulgar fraction) [n 1] is a rational number written as a/b or ⁠ ⁠, where a and b are both integers. [9] As with other fractions, the denominator ( b ) cannot be zero.

  6. Irreducible fraction - Wikipedia

    en.wikipedia.org/wiki/Irreducible_fraction

    The notion of irreducible fraction generalizes to the field of fractions of any unique factorization domain: any element of such a field can be written as a fraction in which denominator and numerator are coprime, by dividing both by their greatest common divisor. [7] This applies notably to rational expressions over a field. The irreducible ...

  7. Erdős–Straus conjecture - Wikipedia

    en.wikipedia.org/wiki/Erdős–Straus_conjecture

    As with fractions of the form , it has been conjectured that every fraction (for >) can be expressed as a sum of three positive unit fractions. A generalized version of the conjecture states that, for any positive k {\displaystyle k} , all but finitely many fractions k n {\displaystyle {\tfrac {k}{n}}} can be expressed as a sum of three ...

  8. List of unsolved problems in mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.

  9. Natural number - Wikipedia

    en.wikipedia.org/wiki/Natural_number

    For example, the integers are made by adding 0 and negative numbers. The rational numbers add fractions, and the real numbers add infinite decimals. Complex numbers add the square root of −1. This chain of extensions canonically embeds the natural numbers in the other number systems. [6] [7] Natural numbers are studied in different areas of math.

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