What is mean by natural numbers?

Answer 1

positive integers. 1,2,3,4,5....

Answer 2

The natural numbers are the positive integers, and depending on whom you ask, also 0.
Therefore they are either {1, 2, 3, 4, 5, 6, . . .}
or {0, 1, 2, 3, 4, 5, 6, . . . }

The natural numbers are denoted by N.

Personally I like to include 0, because the set of positive numbers is already clearly defined by Z+, but it is up to taste. The inclusion or exclusion of 0 will not change any results, and will only slightly change proofs or statements of theorems.

Answer 3

1, 2, 3, 4, 5, 6, ...

It originally does not include the zero and negative numbers.

However, some set theory and computer science had included the number 0 as part of the natural number.

0, 1, 2, 3, 4, 5, 6, ...

Answer 4

Now that can be a very interesting question.

Briefly: the set of all Natural Numbers (denoted by N) is the set of all counting numbers {1,2,3,4,5,6,7,8....}

It has been recently discovered that the concept of Natural Numbers (or Counting) is known by both dogs, chimpanzees and gorrillas. Zoologists have done experiments, and apparently the concept of Natural Numbers {1,2,3,4,5,6,7,8....} is something that is intuitively known. Which brings up the question: Are Natural Numbers Real? (Mathematicians will get my pun). That is: are Natural Numbers NOT something that was artificially created by human minds, but is something that exists independently of human thought and is somehow built into the rules, which underlie physical laws which govern our universe?

Think of Natural Numbers as the set of all counting numbers {1,2,3,4,5,6,7,8....}

Whole Numbers as the set of all Natural Numbers union {0}. or W = [0} U {1,2,3,4,5,6,7,8....}. Thus
N is a subset of W

The Integers are an extension of the Whole Numbers (W)
Integers denoted by Z
Z = {..,-4,-3,-2,-1,0,1,2,3,4,...}

So W is a subset of Z

The Rational Numbers (denoted by Q) are your fractions: that is: Q ={m/n: m,n are elements of Z, such that n is NOT equal to 0}

Real Numbers are the set of all Rational Numbers and Irrational Numbers. (an Irrational Number is any number that cannot be expressed as a fraction)
(as an Aside there are 2 classes of Irrational Numbers: Algebraic Irrational Numbers, and Transcendental Irrational Numbers)

A further extension of Real Numbers leads us to the Complex Number set.

One of the key elements in Mathematics was linking points on a line to the Real Numbers.
(and points on the Complex plane to Complex Numbers).
which lead to the marriage of algebra and geometry.
(thank you Rene Descarte)

But I digress: The Natural Numbers have many interesting properties. And all Natural numbers are broken into 2 classes: Prime Numbers and Composite Numbers.
All Composite Numbers can be generated by a finite product of Prime Numbers..
For example: 6 is a composite number
6=2*3 the product of two prime numbers.
9 is a composite number
9=3*3 (or 3^2)

Prime Numbers are any Natural Number greater than 1 that is divisible only by 1 or itself.

Thus the set of Prime Numbers are: {2,3,5,7,11,13,....}

2 is the only even Prime Number.

I think prime numbers and composite numbers are natural to the universe (no pun intended)

(Edited to Add: It is an excersize in books on Set Theory to construct the set of Natural Numbers from the Null Set)


To paraphrase a famous Mathematician: "God made Integers, all else are the handiwork of Man"

Answer 5

numbers starting with 1 not including zero are known as natural numbers

Answer 6

It is any non-negative number-- 0, 1, 2, 3, 4......

Answer 7

Positive integers (whole numbers): 1, 2, 3, etc.

Answer 8

Natural Numbers, the numbers we use fokr counting. N={1,2,3,4,5,6,7,8,9,10,11, . . .} The three dots, called the elipsis indicate that the list continues on forever.

Answer 9

counting numbers... 1, 2, 3,...

Answer 10

natural numbers are {0,infinity)

Answer 11

123456........BUT NOT 0 AS 0123456......ARE SET OF WHOLE NUMBERS.