In category theory, a natural numbers object (NNO) is an object endowed with a recursive structure similar to natural numbers. More precisely, in a category...

mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative...

assignments of natural numbers to mathematical objects. Gödel noted that each statement within a system can be represented by a natural number (its Gödel...

−2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative integers. The set of all integers is often...

over natural numbers are a mathematical model used in studying computational complexity theory. They are a special case of circuits. The object is a labeled...

M a t {\displaystyle \mathbf {Mat} } , is the category whose objects are natural numbers and whose morphisms are matrices, with composition given by matrix...

prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is...

Commonly encountered mathematical objects include numbers, expressions, shapes, functions, and sets. Mathematical objects can be very complex; for example...

adjectives, or adverbs that designate numbers. The distinction is drawn between the number five (an abstract object equal to 2+3), and the numeral five...

rig of natural numbers N is an initial object. The zero rig, which is the zero ring, consisting only of a single element 0 = 1 is a terminal object. In Field...

natural numbers using computable functions, to these different types of objects. A simple extension is to assign cardinal numbers to physical objects...

In set theory, several ways have been proposed to construct the natural numbers. These include the representation via von Neumann ordinals, commonly employed...

The Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. They are named...

{\displaystyle {\mathsf {Sets}}\to {\mathsf {Eff}}} . The topos has a natural numbers object N = ⟨ N , E N ⟩ {\displaystyle N=\langle {\mathbb {N} },E_{\mathbb...

each object the size of the initial segment with that object as last element. Note that these numbers are one more than the formal ordinal numbers according...

mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented...

objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers....

as a category, PER models are a cartesian closed category with natural numbers object and subobject classifier, giving rise to the effective topos introduced...

In natural language and physical science, a physical object or material object (or simply an object or body) is a contiguous collection of matter, within...

mathematical object. For another axiomatization of R {\displaystyle \mathbb {R} } see Tarski's axiomatization of the reals. The real numbers can be constructed...

as referees "1" and "2" is a use of nominal numbers. Any set of numbers (a subset of the natural numbers) will be consistent labels as long as a distinct...

Ordinal Numbers (1958, 2nd ed. 1965). Any finite natural number can be used in at least two ways: as an ordinal and as a cardinal. Cardinal numbers specify...

some set of mathematical elements—natural numbers, real numbers, functions, relations, systems—are such abstract objects. Contrarily, mathematical nominalism...

recursive functions. In realzability topoi, this exponential object of the natural numbers object can also be identified with less restrictive collections...

Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th-century Italian mathematician Giuseppe Peano...

Object-oriented programming (OOP) is a programming paradigm based on the concept of objects. Objects can contain data (called fields, attributes or properties)...

in scope and may refer to animals; natural features such as mountains; inanimate objects such as tables; numbers or sets as symbols written on a paper;...

all square roots of natural numbers, other than of perfect squares, are irrational. Like all real numbers, irrational numbers can be expressed in positional...

formulations regarding finite objects tends to not differ from their classical counterparts. Given a model of all natural numbers, the equivalent for predicates...

and an Ontology of Natural Numbers in Isabelle/HOL (PhD thesis). Free University of Berlin. Zalta, Edward N. (May 2020). "Typed object theory" (PDF). In...