arithmetical set (or arithmetic set) is a set of natural numbers that can be defined by a formula of first-order Peano arithmetic. The arithmetical sets...

certain sets based on the complexity of formulas that define them. Any set that receives a classification is called arithmetical. The arithmetical hierarchy...

types of arithmetic. Modular arithmetic operates on a finite set of numbers. If an operation would result in a number outside this finite set then the...

of memory, but most RISC instruction sets include SIMD or vector instructions that perform the same arithmetic operation on multiple pieces of data at...

scheme for arithmetical formulas (which is sometimes called the "arithmetical comprehension axiom"). That is, ACA0 allows us to form the set of natural...

mathematics, modular arithmetic is a system of arithmetic operations for integers, other than the usual ones from elementary arithmetic, where numbers "wrap...

interpreting the arithmetic progression as a set of equally probable outcomes. The product of the members of a finite arithmetic progression with an...

variables (that is, no quantifiers over set variables) is called arithmetical. An arithmetical formula may have free set variables and bound individual variables...

In mathematical logic and descriptive set theory, the analytical hierarchy is an extension of the arithmetical hierarchy. The analytical hierarchy of formulas...

set generalizes this idea to multiple dimensions – it is a set of vectors of integers, rather than a set of integers. A finite generalized arithmetic...

example, the set {1} is both a member and a proper subset of the set {1, {1}}. Just as arithmetic features binary operations on numbers, set theory features...

Schröder. The Peano axioms define the arithmetical properties of natural numbers, usually represented as a set N or N . {\displaystyle \mathbb {N} .}...

collection. The collection is often a set of results from an experiment, an observational study, or a survey. The term "arithmetic mean" is preferred in some contexts...

Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are...

independence proof by forcing automatically proves independence from arithmetical statements, other concrete statements, and large cardinal axioms. Some...

its proof, is an arithmetical relation between two numbers. Therefore, there is a statement form Bew(y) that uses this arithmetical relation to state...

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

In computing, an arithmetic logic unit (ALU) is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers...

Haar null set Convex set Balanced set, Absolutely convex set Fractal set Recursive set Recursively enumerable set Arithmetical set Diophantine set Hyperarithmetical...

definable in the language of arithmetic is called analytical. Every computable real number is arithmetical, and the arithmetical numbers form a subfield of...

In set theory, the complement of a set A, often denoted by A c {\displaystyle A^{c}} (or A′), is the set of elements not in A. When all elements in the...

sets. A set may be finite or infinite. There is a unique set with no elements, called the empty set; a set with a single element is a singleton. Sets...

the empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories...

In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation...

classified into a hierarchy extending the arithmetical hierarchy; the hyperarithmetical sets are exactly the sets that are assigned a rank in this hierarchy...

In mathematics, Robinson arithmetic is a finitely axiomatized fragment of first-order Peano arithmetic (PA), first set out by Raphael M. Robinson in 1950...

computable set of numbers can be defined by some arithmetical formula. For example, there are formulas in the language of arithmetic defining the set of codes...

theory Diophantine set Matiyasevich's theorem Word problem for groups Arithmetical hierarchy Subrecursion theory Presburger arithmetic Computational complexity...

include in their definition the requirement that an arithmetical function "expresses some arithmetical property of n". There is a larger class of number-theoretic...

floating-point units use the IEEE 754 standard. The standard defines: arithmetic formats: sets of binary and decimal floating-point data, which consist of finite...