Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Difference Between these

  1. Jan 22, 2004 #1
    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.

  2. jcsd
  3. Jan 22, 2004 #2
    These are basic definition u would find in any maths book
    Natural Numbers
    1,2,3,4,...... are called Natural Numbers, their set is denoted by N

    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....}
  4. Jan 22, 2004 #3
    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.
  5. Jan 22, 2004 #4
    Yup its true
  6. Jan 22, 2004 #5
    Difference between these

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

  7. Jan 22, 2004 #6
    isn't it denoted by Z???
  8. Jan 22, 2004 #7

    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.

  9. Jan 22, 2004 #8
    0 is a part of N , without it, it would not form a monoid for the addition.
  10. Jan 22, 2004 #9
    Re: ...

    actually no,

    if you want to be picky I was refering to [tex]\mathbb{Z}[/tex] but I was too busy to write the tex code....
    and it's about mathematics not personal preferences :wink:
  11. Jan 22, 2004 #10


    User Avatar
    Science Advisor

    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.
  12. Jan 22, 2004 #11
    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
  13. Jan 22, 2004 #12

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

  14. Jan 22, 2004 #13
    I means imaginary numbers.
  15. Jan 22, 2004 #14
    Both [itex]\mathbb{I}[/itex] and [itex]\mathbb{Z}[/itex] are considered acceptable symbols for the set of integers. [itex]\mathbb{Z}[/itex] 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 [itex]\mathbb{Z}[/itex] because everyone I've ever worked with uses it, and I try to be consistent.
  16. Jan 23, 2004 #15
    yes, [itex]\mathbb{Z}[/itex] rules

    and Tron3k the imaginary numbers are part of the complex numbers [itex]\mathbb{C}[/itex], there is no special symbol for them.
  17. Jan 23, 2004 #16


    User Avatar
    Staff Emeritus
    Gold Member

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook