Integers (पूर्णांक)-     The group of positive and negative whole numbers are called integers.

          Ex-     ..., ^-3, ^-2, ^-1, 0, ⁺1, ⁺2, ⁺3, ... 

The set of all integers is usually denoted by Z or Z+

Digits (अंक) - The 10 symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, are called digits.

Digits are used to create numbers in the base 10 decimal number system.

Total number of digits is 10.

Numbers – Digits and the group of digits are called numbers.

The Arabic numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are used in the Hindu-Arabic number system to define numbers.

Natural Numbers (प्राकृत संख्या)-  The set of counting numbers is called natural number.                       

        Ex- 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,.....,

• Natural numbers are also called positive integers.
• The smallest natural number is one.
• The largest natural number is infinitive.
• The set of natural number is denoted by 'N'. EX- N = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,.....}

Whole Numbers (पूर्ण संख्या) - The natural numbers together with zero are called whole numbers.             

          Ex- 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, ........

• The smallest whole number is zero.
• The largest whole number is infinitive.
• The set of whole number is denoted by 'W'. EX- W = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,.....}

Even Numbers (सम संख्या): -       A number exactly divisible by 2 is called even numbers.

Recognise- Unit’s place of even number may be 0, 2, 4, 6 or 8                    

Ex-    2, 4, 6, 8, 10, 12, 14, 16..........................are even number.

Ex-    246, 1894, 5468, 100 are even number.

• The smallest even number is two.
• The largest even number is infinitive.

Consecutive even number (लगातार सम संख्या): -  Any two even numbers whose difference is 2 are called consecutive even number.

          Ex-    2, 4, 6, 8, 10, 12, 14 etc.

Here-   4 -2 = 6 -4 = 8 - 6 = 10 - 8 = 12 - 10 = 2 

Odd Numbers (विषम संख्या): -      A number which is not exactly divisible by 2 is called an odd number.     

Ex-    3, 5, 7, 9, 11, 13, 15, are odd number.
Recognise- Unit’s place of odd number may be 1, 3, 5, 7 or 9.  

• The smallest odd number is one.
• The largest odd number is infinitive.

Consecutive odd number: -     Any two odd numbers whose difference is 2 are called consecutive odd number.

Prime Numbers (रूढ़ संख्या): -      Numbers which have only two factors namely 1 and itself are called prime numbers.
Ex-    2, 3, 5, 7, 11, 19, 37 etc. are prime numbers.

Note- (a) 1 is not prime number because it has only one factor that is 1.

          (b) 2 is the lowest and the only even prime number.

Composite Numbers (भाज्य संख्या/यौगिक संख्या): -         Numbers having more than two factors are called composite numbers.      

Ex-    4, 6, 8, 9, 10 etc are composite numbers.

Notes:
(a) 1 is neither prime nor composite.
(b) 4 is the lowest even composite number.

(c) 9 is the lowest odd composite number.

Co-prime Numbers (सह अभाज्य संख्या)-  Two numbers which have no common factor except 1is called co-prime numbers.

• Two numbers whose HCF is 1 called co-prime numbers.
• Co-prime numbers need not be prime numbers.
  Ex-    (i) 7 and 10 are co-prime.                   (ii) 15 and 17 are co-prime.

Twin Prime Numbers (जुड़वाँ अभाज्य संख्या): -    Two prime numbers whose difference is 2 are called twin prime numbers.

Ex-    (i) 3 and 5             (ii) 17 and 19                  (iii) 41 and 43                                    (iv) 29 and 31        (v) 71 and 73.

Rational Numbers (परिमेय संख्या) –       A number in the form of p/q where ‘p’ and ‘q’ are integer  but q≠0 is called rational number.

                        

• ‘p’ is called numerator which may be any whole number
• ‘q’ is called denominator which may be any positive whole number greater than zero.
• If the denominator happens to be unity, q = 1, the ratio is an integer.
• If "q" is other than 1, p/q is a fraction.

Irrational Numbers (अवास्तविक संख्या): -    Those numbers that can’t be written as a fraction is called Irrational numbers.

     Ex-     ,  and  

Note-           is not irrational number because it’s value is 2.

Fractional Numbers (भिन्न संख्या)– The part of whole is called fractional number.

Real Numbers (वास्तविक संख्या)- The set of rational and irrational numbers is called real numbers.

          All the real numbers can be written in a finite or infinite decimal form, such as  =1.414213562…… and Pai  .

Square of number (संख्या का वर्ग): -       When a number is multiplied by itself then obtained number is called square of that number.

• Square of x is written in the form  .
• Square of 5 = 5² = 5×5 = 25

Square Number (वर्ग संख्या): -     Square Numbers are integers that can be written as the square of other integers, ie. a product of an integer multiplied by itself.

Ex-     4, (2×2), 9, (3×3), 16, (4×4) and 25, (5×5)

Surds (करणी) -       The numbers in the form ofn, where n is a positive integer that is not a square number is called surd.   

EX-   , , and