# Difference Between these

1. Jan 22, 2004

### 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.

2. Jan 22, 2004

### 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....}

3. Jan 22, 2004

### 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?
Info.

4. Jan 22, 2004

### himanshu121

Yup its true

5. Jan 22, 2004

### info.edp

Difference between these

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

Info.

6. Jan 22, 2004

### Guybrush Threepwood

isn't it denoted by Z???

7. Jan 22, 2004

### sridhar_n

...

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

8. Jan 22, 2004

### Kalimaa23

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

9. Jan 22, 2004

### Guybrush Threepwood

Re: ...

actually no,

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

10. Jan 22, 2004

### HallsofIvy

Staff Emeritus
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.

11. Jan 22, 2004

### 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
So its upto U what u want it to assign

Though I agree Z can also be used

12. Jan 22, 2004

### sridhar_n

...

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

Sridhar

13. Jan 22, 2004

### Tron3k

I means imaginary numbers.

14. Jan 22, 2004

### 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.

15. Jan 23, 2004

### Guybrush Threepwood

yes, $\mathbb{Z}$ rules

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

16. Jan 23, 2004

### ahrkron

Staff Emeritus
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.