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  2. 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.

  3. List of numeral systems - Wikipedia

    en.wikipedia.org/wiki/List_of_numeral_systems

    It also forms the basis for the Peano axioms for formalizing arithmetic within mathematical logic. A form of unary notation called Church encoding is used to represent numbers within lambda calculus. Some email spam filters tag messages with a number of asterisks in an e-mail header such as X-Spam-Bar or X-SPAM-LEVEL. The larger the number, the ...

  4. List of types of numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_numbers

    Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.

  5. Radix - Wikipedia

    en.wikipedia.org/wiki/Radix

    Radices are usually natural numbers. However, other positional systems are possible, for example, golden ratio base (whose radix is a non-integer algebraic number), [5] and negative base (whose radix is negative). [6] A negative base allows the representation of negative numbers without the use of a minus sign. For example, let b = −10.

  6. Numeral system - Wikipedia

    en.wikipedia.org/wiki/Numeral_system

    A number has a terminating or repeating expansion if and only if it is rational; this does not depend on the base. A number that terminates in one base may repeat in another (thus 0.3 10 = 0.0100110011001... 2). An irrational number stays aperiodic (with an infinite number of non-repeating digits) in all integral bases.

  7. Golden ratio base - Wikipedia

    en.wikipedia.org/wiki/Golden_ratio_base

    No non-integer rational number can be represented as a finite base-φ number. In other words, all finitely representable base-φ numbers are either integers or (more likely) an irrational in a quadratic field Q[√ 5]. Due to long division having only a finite number of possible remainders, a division of two integers (or other numbers with ...

  8. Non-standard positional numeral systems - Wikipedia

    en.wikipedia.org/wiki/Non-standard_positional...

    In some systems, while the base is a positive integer, negative digits are allowed. Non-adjacent form is a particular system where the base is b = 2.In the balanced ternary system, the base is b = 3, and the numerals have the values −1, 0 and +1 (rather than 0, 1 and 2 as in the standard ternary system, or 1, 2 and 3 as in the bijective ternary system).

  9. Unary numeral system - Wikipedia

    en.wikipedia.org/wiki/Unary_numeral_system

    It also forms the basis for the Peano axioms for formalizing arithmetic within mathematical logic. [18] A form of unary notation called Church encoding is used to represent numbers within lambda calculus. [19] Some email spam filters tag messages with a number of asterisks in an e-mail header such as X-Spam-Bar or X-SPAM-LEVEL. The larger the ...