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satisfies some arithmetical property. A set Y of natural numbers is implicitly arithmetical or implicitly arithmetically definable if it is definable with an...

In number theory, an arithmetic, arithmetical, or number-theoretic function is generally any function f(n) whose domain is the positive integers and whose...

elementary function arithmetic (EFA), also called elementary arithmetic and exponential function arithmetic, is the system of arithmetic with the usual...

of arithmetically definable functions is closed under primitive recursion, and therefore includes all primitive recursive functions. The β function was...

have only countably many formulas, every notion of definable numbers has at most countably many definable real numbers. However, by Cantor's diagonal argument...

In number theory, the gcd-sum function, also called Pillai's arithmetical function, is defined for every n {\displaystyle n} by P ( n ) = ∑ k = 1 n gcd...

OEIS). In number theory another arithmetic function closely related to the Möbius function is the Mertens function, defined by M ( n ) = ∑ k = 1 n μ ( k...

lower in the arithmetical hierarchy. Post's theorem shows that, for each n, Thn( N {\displaystyle {\mathcal {N}}} ) is arithmetically definable, but only...

(also arithmetic and arithmetically definable) if it is defined by some formula in the language of Peano arithmetic. Equivalently X is arithmetical if X...

mathematics, the arithmetic zeta function is a zeta function associated with a scheme of finite type over integers. The arithmetic zeta function generalizes...

than it. If elements in the data increase arithmetically when placed in some order, then the median and arithmetic average are equal. For example, consider...

In number theory, the Lagarias arithmetic derivative or number derivative is a function defined for integers, based on prime factorization, by analogy...

cohomology of Spec K. Two fields are called arithmetically equivalent if they have the same Dedekind zeta function. Wieb Bosma and Bart de Smit (2002) used...

directly characterized by height functions which measure their arithmetic complexity. The structure of algebraic varieties defined over non-algebraically closed...

\Re (z)>0\,.} The gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic in...

common example of a sigmoid function is the logistic function shown in the first figure and defined by the formula: σ ( x ) = 1 1 + e − x = e x 1 + e x...

In computer programming, a pure function is a function that has the following properties: the function return values are identical for identical arguments...

A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support...

[citation needed] Sign function Three-way comparison Might not be present in a Fortran 2018 compiler. See the Deprecation section. arithmetic IF @ everything2...

axioms define the arithmetical properties of the natural numbers. The naturals are assumed to be closed under a single-valued "successor" function S. For...