**natural numbers** — plural noun The whole numbers 1, 2, 3 and upwards, sometimes also including 0 • • • Main Entry: ↑natural … Useful english dictionary

**natural numbers** — whole numbers from 1 and up … English contemporary dictionary

**natural numbers** — plural noun the positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well … English new terms dictionary

**natural numbers** — noun a) The set of positive integers, 1, 2, 3, .... 0∈ℕ, and b) The set of non negative integers, ℕ = 0, 1, 2, 3, ..., being the smallest such that: n∈ℕ⇒ succ(n)∈ℕ … Wiktionary

**Circuits over sets of natural numbers** — Circuits over natural numbers is a mathematical model used in studying computational complexity theory. It is a special case of circuit, the object is a labeled directed acyclic graph the nodes of which evaluate to sets of natural numbers, the… … Wikipedia

**Addition of natural numbers** — is the most basic arithmetic binary operation. The operation addition takes two natural numbers, the augend and addend, and produces a single number, the sum. The set of natural numbers will be denoted by N, and 0 will be used to denote the… … Wikipedia

**Addition of natural numbers/Proofs** — Mathematical proofs for addition of the natural numbers: additive identity, commutativity, and associativity. These proofs are used in the article Addition of natural numbers.DefinitionsThis article will use the definitions in addition of natural … Wikipedia

**Set-theoretic definition of natural numbers** — Several ways have been proposed to define the natural numbers using set theory.The contemporary standardIn standard (ZF) set theory the natural numbersare defined recursively by 0 = {} (the empty set) and n +1 = n ∪ { n }. Then n = {0,1,..., n… … Wikipedia

**Natural number** — Natural numbers can be used for counting (one apple, two apples, three apples, ...) from top to bottom. In mathematics, the natural numbers are the ordinary whole numbers used for counting ( there are 6 coins on the table ) and ordering ( this is … Wikipedia

**Natural** — Nat u*ral (?; 135), a. [OE. naturel, F. naturel, fr. L. naturalis, fr. natura. See {Nature}.] 1. Fixed or determined by nature; pertaining to the constitution of a thing; belonging to native character; according to nature; essential;… … The Collaborative International Dictionary of English