recursive numbers, effective numbers, computable reals, or recursive reals. The concept of a computable real number was introduced by Émile Borel in 1912...

of computability that can be imagined can compute only functions that are computable in the above sense. Before the precise definition of computable functions...

natural numbers is computable. The empty set is computable. The entire set of natural numbers is computable. Every natural number is computable. The subset of...

thus also not arithmetical. Every computable number is arithmetical, but not every arithmetical number is computable. For example, the limit of a Specker...

algebraic numbers. The computable numbers may be viewed as the real numbers that may be exactly represented in a computer: a computable number is exactly represented...

partial functions is computable if the relation R(x,y,z) = "[g(x)](y) = z" is partial recursive (Ershov 1999:487). A computable numbering is called principal...

recognize. The domain of any universal computable function is a computably enumerable set but never a computable set. The domain is always Turing equivalent...

Enumerability: The set S is the range of a partial computable function. The set S is the range of a total computable function, or empty. If S is infinite, the...

Church–Turing thesis, which states that any function that is computable by an algorithm is a computable function. Although initially skeptical, by 1946 Gödel...

basis of clopen groups so the space is zero-dimensional. Brjuno number Computable number Diophantine approximation Irrationality measure Proof that e is...

of computable functions. It states that a function on the natural numbers can be calculated by an effective method if and only if it is computable by...

to practical computation... (Hodges p. 124) 1 computable number — a number whose decimal is computable by a machine (i.e., by finite means such as an...

Any non-computable number, in particular: Chaitin's constant. Constructed irrational numbers which are not simply normal in any base. Any number for which...

numbers by expressions such as π·sin(2), and can thus represent any computable number with infinite precision. A common application is public-key cryptography...

upon below. Type 1 computability is the naive form of computable analysis in which one restricts the inputs to a machine to be computable numbers instead...

with weights. Computable number: A real number whose digits can be computed by some algorithm. Period: A number which can be computed as the integral...

computability theory, a function is called limit computable if it is the limit of a uniformly computable sequence of functions. The terms computable in...

language Word problem for groups Wang tile Penrose tiling Computable number Definable number Halting probability Algorithmic information theory Algorithmic...

code examples demonstrating access and use of IEEE 754 features. Computable number Coprocessor Decimal floating point Double-precision floating-point...

verification that g is computable relies on the following constructs (or their equivalents): computable subprograms (the program that computes f is a subprogram...

In computing, a normal number is a non-zero number in a floating-point representation which is within the balanced range supported by a given floating-point...

and compass construction problem put forth by Pappus. Computable number Definable real number Kazarinoff (2003), pp. 10, 15; Martin (1998), p. 41, Corollary...

possible to construct artificial examples of computable numbers which are not periods. However there are no computable numbers proven not to be periods, which...

Turing machine capable of computing any computable sequence, as described by Alan Turing in his seminal paper "On Computable Numbers, with an Application...

a reduction computable by a deterministic Turing machine using logarithmic space. Conceptually, this means it can keep a constant number of pointers into...

partial computable functions. Such enumerations are formally called computable numberings of the partial computable functions. An arbitrary numbering η of...

\to \mathbb {N} } is any computable function, then Σ(n) > f(n) for all sufficiently large n, and hence that Σ is not a computable function. Moreover, this...

domain ω and only countably many computable functions. A specific example of a set with an enumeration but not a computable enumeration is the complement...

fixed Gödel numbering of partial computable functions. Let φ e {\displaystyle \varphi _{e}} be a computable enumeration of all partial computable functions...

NPA hierarchy to produce a halting algorithm to compute the Tsirelson bound, making it a computable number (note that in isolation neither procedure halts...