Math Is Fun Forum

coolboyx12

Member

Registered: 2023-03-10

Posts: 34

Natural number definition

I thought i knew what natural numbers were, numbers excluding zero and the negative numbers but my book says that natural numbers include 0, but byjus says that natural numbers dont include zero, some say they do and some say they dont and chatgpt just says, well this : The terminology around natural numbers and whole numbers can vary slightly depending on the context or educational system. In some definitions, natural numbers are defined as the positive integers starting from 1, while in others, they include 0 as well.

Traditionally, natural numbers referred to the counting numbers
1
,
2
,
3
,
4
,
…
1,2,3,4,… and did not include zero. This definition was prevalent in older mathematical literature and some educational systems.

However, in modern mathematics and many educational curricula, the term "natural numbers" often includes zero, thus encompassing the entire set of non-negative integers
0
,
1
,
2
,
3
,
…
0,1,2,3,…. This broader definition is more inclusive and aligns with the concept of natural numbers being the numbers we use for counting, starting from zero.

On the other hand, "whole numbers" are generally understood to include zero along with the positive integers. So, while there might be some variation in definitions between different sources or educational systems, it's important to understand the context in which these terms are being used. Ultimately, the distinction between natural numbers and whole numbers may vary depending on the specific curriculum or educational material being used.   (Im confused help me!!).

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It pays to keep an open mind, but not so open your brains fall out. - Carl Sagan.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,267

Re: Natural number definition

Hi coolboyx12,

Definition of Natural Number :

Google: Natural numbers are all positive integers from 1 to infinity. They are also called counting numbers as they are used to count objects. Natural numbers do not include 0 or negative numbers. We need numbers in our everyday life, be it for counting objects, telling time, or numbering houses.

Wikipedia : In mathematics, the natural numbers are the numbers 1, 2, 3, etc., possibly including 0 as well. Some definitions, including the standard ISO 80000-2, begin the natural numbers with 0, corresponding to the non-negative integers 0, 1, 2, 3, ..., whereas others start with 1, corresponding to the positive integers 1, 2, 3, ... Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). In common language, particularly in primary school education, natural numbers may be called counting numbers to intuitively exclude the negative integers and zero, and also to contrast the discreteness of counting to the continuity of measurement—a hallmark characteristic of real numbers.

Britannica: Natural numbers

In a collection (or set) of objects (or elements), the act of determining the number of objects present is called counting. The numbers thus obtained are called the counting numbers or natural numbers (1, 2, 3, …). For an empty set, no object is present, and the count yields the number 0, which, appended to the natural numbers, produces what are known as the whole numbers.

If objects from two sets can be matched in such a way that every element from each set is uniquely paired with an element from the other set, the sets are said to be equal or equivalent. The concept of equivalent sets is basic to the foundations of modern mathematics and has been introduced into primary education, notably as part of the “new math”  that has been alternately acclaimed and decried since it appeared in the 1960s.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

coolboyx12

Member

Registered: 2023-03-10

Posts: 34

Re: Natural number definition

so which one is right or is it a matter of choice between accepting 0 in natural numbers and not, and yeah, the book is CAIE IGCSE Math, which can't be wrong(right?), so what am i supposed to do, can i choose or do i have to go with one or the other and apart from Wikipedia and all that, what are your personal views on this.

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It pays to keep an open mind, but not so open your brains fall out. - Carl Sagan.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,169

Re: Natural number definition

This can (and does) happen in other branches of mathematics.  There's no absolute authority that determines definitions and anyone can write a book developing an area of maths using whatever definitions they like.

eg.  Is 0.999999 recurring the same as 1 ?

Many say yes and use this as a way to convert recurring decimals into fractions for example.  But I have a maths text that avoids the question completely by declaring that decimals 'ending' with a recurring set of 9s as being invalid real numbers.  So 1 exists but 0.99999 recurring doesn't.

There is also a question about how to define parallel lines: two lines that make the same angle with a transversal or two lines that never meet when extended indefinitely. This arose recently in a post about Euclidean geometry.

The Edexcel exam board avoids this issue completely by only requiring a knowledge of integers. I assume this means that 'natural numbers' and 'whole numbers' are never used in exam questions.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

coolboyx12

Member

Registered: 2023-03-10

Posts: 34

Re: Natural number definition

well anyways, i grew up always thinking that the set of numbers {0,1,2,3....} was the set of whole numbers and the set of numbers {1,2,3.....} was the set of natural numbers, so i was really confused that a prestigious board such as CAIE
(Cambridge Assessment International Education) would say something like this, this their whole statement word for word: Natural numbers
A child learns to count ‘one, two, three, four, …’. These are sometimes
called the counting numbers or whole numbers.
The child will say ‘I am three’, or ‘I live at number 73’.
If we include the number 0, then we have the set of numbers called the
natural numbers.
The set of natural numbers N = {0, 1, 2, 3, 4, …}.

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It pays to keep an open mind, but not so open your brains fall out. - Carl Sagan.

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Natural number definition

so which one is right or is it a matter of choice between accepting 0 in natural numbers and not, and yeah, the book is CAIE IGCSE Math, which can't be wrong(right?), so what am i supposed to do, can i choose or do i have to go with one or the other and apart from Wikipedia and all that, what are your personal views on this.

Use whatever definition they use in your current class/book
If they use a different def. in your next class/book then use *that* def
Yes it can be confusing