What are the differences between natural, rational, whole, and integer numbers?

[info.edp]

What are the differences between all of these numbers
- Natural Numbers.
- Rational Numbers.
- Whole Numbers.
- Integers.

Can anyone explain these with definitions and examples.

Thanks for the help.

Info.

 

[himanshu121]

These are basic definition u would find in any maths book
still
Natural Numbers
1,2,3,4,... are called Natural Numbers, their set is denoted by N

Integers
The Number ...-3,-2,-1,0,1,2,3... are called integers and their set is denoted by I

Rational Numbers

All numbers of the form p/q where p&q are integers and q not equal to 0 are called rational numbers and their set is denoted by Q and H.C.F of p,q is 1

Whole Numbers

Set of non-negative integers {0,1,2,3...}

 

[info.edp]

Thanks for the reply. Why is 0 not included in the set of Natural Numbers? Is it true that 0 has its origin from India?

Any ideas?
Thanks in advance.
Info.

 

[himanshu121]

Is it true that 0 has its origin from India?

Yup its true

 

[info.edp]

Difference between these

What about 0 not included in the set of Natural Numbers?

Info.

 

[Guybrush Threepwood]

Originally posted by himanshu121
Integers
The Number ...-3,-2,-1,0,1,2,3... are called integers and their set is denoted by I

isn't it denoted by Z?

 

[sridhar_n]

...

isn't it denoted by Z?

Doesn't Z denote a Complex functions?


I personally feel that using Ifor the set of integers is more convinient than using any other alphabet.


Sridhar

 

[Kalimaa23]

0 is a part of N , without it, it would not form a monoid for the addition.

 

[Guybrush Threepwood]

Originally posted by sridhar_n
Doesn't Z denote a Complex functions?

actually no,

I personally feel that using Ifor the set of integers is more convinient than using any other alphabet.

if you want to be picky I was referring to $$\mathbb{Z}$$ but I was too busy to write the tex code...
and it's about mathematics not personal preferences

 

[HallsofIvy]

As to whether 0 is a natural number or not: it's a matter of taste. Peano's axioms originally included 0. Most modern math books identify "natural numbers" with "counting numbers" and start with 1.

It is true that the "counting numbers" do not form a monoid.
The "whole numbers" do.

 

[himanshu121]

Sridhar we can use Z too for integers we here in India do use I for integers, and is much more convenient here But I want to quote this
for GuyBrush

Symbol/Notation doesn't mean anything unless u know what do Symbol/notation represents

So its upto U what u want it to assign

Though I agree Z can also be used

 

[sridhar_n]

...

Thats what I have been telling him Himanshu...I is a more convenient notation for Integers...

Sridhar

 

[Tron3k]

I means imaginary numbers.

 

[master_coda]

Both $\mathbb{I}$ and $\mathbb{Z}$ are considered acceptable symbols for the set of integers. $\mathbb{Z}$ is the most commonly used symbol, primarily for historical reasons. It's also traditional to use double-stuck characters, although that is just a convention as well.

However, neither symbol is better. The matter is entirly subjective. I use $\mathbb{Z}$ because everyone I've ever worked with uses it, and I try to be consistent.

 

[Guybrush Threepwood]

Originally posted by master_coda
I use $\mathbb{Z}$ because everyone I've ever worked with uses it, and I try to be consistent. [/B]

yes, $\mathbb{Z}$ rules

and Tron3k the imaginary numbers are part of the complex numbers $\mathbb{C}$, there is no special symbol for them.

 

[ahrkron]

I sometime heard that Z is used for integers because the german word for "integer" starts with Z, so it was natural choice for the many german mathematicians working with them.