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en.wikipedia.org/wiki/Natural_number

The first ordinal number that is not a natural number is expressed as ω; this is also the ordinal number of the set of natural numbers itself. Many well-ordered sets with cardinal number ℵ 0 have an ordinal number greater than ω (the latter is the lowest possible). The least ordinal of cardinality ℵ 0 (i.e., the initial ordinal) is ω.

mathworld.wolfram.com/NaturalNumber.html

In fact, Ribenboim (1996) states "Let be a set of natural numbers; whenever convenient, it may be assumed that ." The set of natural numbers (whichever definition is adopted) is denoted N. Due to lack of standard terminology, the following terms and notations are recommended in preference to "counting number," "natural number," and "whole number."

whatis.techtarget.com/definition/natural-number

A natural number is a number that occurs commonly and obviously in nature. As such, it is a whole, non-negative number. The set of natural numbers, denoted N, can be defined in either of two ways:

study.com/academy/lesson/what-are-natural-numbers...

The natural numbers are simply the counting numbers you first learned as a child. In this lesson, you will learn a little about the natural numbers, as well as a little about the confusion ...

www.statisticshowto.datasciencecentral.com/natural-number

The set of natural numbers isn’t closed under subtraction or division. For every natural number a, there exist natural numbers b and c such that a – b = e and a / c = f, where e and f are not natural numbers. Natural numbers make an infinite set. For any natural number, there is another natural number that is one greater.

www.math-only-math.com/standard-sets-of-numbers.html

The standard sets of numbers can be expressed in all the three forms of representation of a set i.e., statement form, roster form, set builder form. 1. N = Natural numbers

www.sangakoo.com/en/unit/set-of-numbers-real-integer...

Set of numbers (Real, integer, rational, natural and irrational numbers) In this unit, we shall give a brief, yet more meaningful introduction to the concepts of sets of numbers, the set of real numbers being the most important, and being denoted by $$\mathbb{R}$$.

www.thoughtco.com/understanding-classification-of-numbers...

Natural numbers are what you use when you are counting one to one objects. You may be counting pennies or buttons or cookies. When you start using 1,2,3,4 and so on, you are using the counting numbers or to give them a proper title, you are using the natural numbers.

mathworld.wolfram.com/N.html

The set of natural numbers (the positive integers Z-+ 1, 2, 3, ...; OEIS A000027), denoted N, also called the whole numbers. Like whole numbers, there is no general agreement on whether 0 should be included in the list of natural numbers. Due to lack of standard terminology, the following terms are recommended in preference to "counting number," "natural number," and "whol...

www.varsitytutors.com/hotmath/hotmath_help/topics/number...

The sum of any two natural numbers is also a natural number (for example, 4 + 2000 = 2004), and the product of any two natural numbers is a natural number (4 × 2000 = 8000). This is not true for subtraction and division, though. The Integers . The integers are the set of real numbers consisting of the natural numbers, their additive inverses ...