Natural numbers: - When we begin to count 1, 2, 3, 4, 5, 6, 7, .... to infinity etc numbers comes naturally before us hence, mathematicians call the counting numbers as Natural numbers.
Collection of Natural Numbers is denoted by Capital N.
N = { 1, 2, 3, 4, 5, 6, 7, ……… ∞}
Whole Numbers: - The natural numbers along with zero form the collection of whole numbers i.e. 0, 1, 2, 3, 4, 5, 6, 7, .... ∞
Collection of Whole Numbers is denoted by Capital W.
W = { 0, 1, 2, 3, 4, 5, 6, 7, ………∞}
Integer: - The set of Negative and Positive whole numbers including zero is called Integer. Collection of Integers is denoted by Capital Z.
Z = {–∞, ..….., – 3, – 2, – 1, 0, + 1, + 2 +3, ………, +∞}
There are two types of integer number.
01. Negative integer: - The integer with Negative sign and started from – ∞ to – 1 is called Negative Integers i.e. –∞, ..….., – 3, – 2, – 1
02. Zero: - Integer 0 is neither negative nor positive.
03. Positive integer: - The integer with positive number started from 1 to ∞ is called Positive Integers i.e. + 1, + 2, + 3, ……, +
Rational Number: - The number in the form of p/q is called Rational number where q ≠ 0 and p and q are integer.
There are two types of rational number.
01. Negative Rational Number: - A rational number is said to be Negative if either its Numerator or Denominator is Negative are Negative Rational Numbrs
02. Zero Rational Number: - 0 is a rational Number because it can be written in the form of with non zero q ≠ 0.
03. Positive Rational Number: - A rational number is said to be positive if its Numerator and Denominator both are Negative or Positive., , 2, 91, are Positive
Note that: - Division by 0 is not define (m/0 = ∞) and m/0 = and Division to 0 by any rational number is zero (0/m = 0)
(i) m/0 = ∞
(ii) 0/m = 0
There are two types of Rational Numbers.
01. Terminating rational number and
02. Non terminating rational number
01. Terminating Rational Numbers: - Which number divided completely by denominator is called Terminating Rational Number. As etc.
02. Non-Terminating Number: - In which rational numbers, the division process never does not comes to end are called Non-Terminating Number.
These are of two types
a) Non-Terminating Repeating Numbers and
b) Non-Terminating Repeating Non Repeating
a) Non-Terminating Repeating Numbers or Non Terminating Recurring Numbers: - In which Non terminating numbers in the division process reminder starts repeating after a certain numbers are called Non Terminating Repeating Numbers or Non Terminating Recurring Numbers.
These Repeating Numbers are represented by putting a bar over the first block or group or pair and other repeating parts of number will omit after putting a Bar.
When reminder repeats itself then you should understand that the quotient repeats itself.
b) Non-Terminating and Non Repeating Numbers: - In which Non terminating numbers, in the division process reminder starts repeating after a certain numbers are called Non Terminating and Non Repeating Numbers.
Irrational Number: - The real numbers that are not expressible in the form of p/q is called Irrational number where q ≠ 0 and p and q are integer.
Pi is an irrational number.
In Typs
1. Natural numbers
Ways to write numbers in different languages
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