Natural numbers
,Natural numbers are the counting
numbers that start from 1 and go on
infinitely.
Definition:
Natural numbers are positive integers
starting from 1 and increasing without an
end. They are denoted by the symbol ℕ.
Set of Natural Numbers:
ℕ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...}
(continues infinitely)
Properties of Natural Numbers:
1. Closure Property – The sum or
product of two natural numbers is
always a natural number.
Example: 3 + 5 = 8, 2 × 4 = 8 (both
are natural numbers).
2. Associative Property – (a + b) + c = a +
(b + c) and (a × b) × c = a × (b × c).
Example: (2 + 3) + 4 = 2 + (3 + 4).
, 3. Commutative Property – a + b = b + a
and a × b = b × a.
Example: 4 + 6 = 6 + 4, 5 × 3 = 3 ×
5.
4. Identity Property –
Addition: a + 0 = a (0 is the
additive identity).
Multiplication: a × 1 = a (1 is the
multiplicative identity).
5. No Negative or Fractional Numbers
– Natural numbers do not include
negative numbers, fractions, or
decimals.
Types of Natural Numbers:
1. Even Natural Numbers – Numbers
divisible by 2: {2, 4, 6, 8, 10, ...}
2. Odd Natural Numbers – Numbers
not divisible by 2: {1, 3, 5, 7, 9, ...}
3. Prime Numbers – Numbers that
, have only two factors (1 and itself),
e.g., {2, 3, 5, 7, 11, 13, ...}.
4. Composite Numbers – Numbers
with more than two factors, e.g., {4,
6, 8, 9, 10, ...}.
,Natural numbers are the counting
numbers that start from 1 and go on
infinitely.
Definition:
Natural numbers are positive integers
starting from 1 and increasing without an
end. They are denoted by the symbol ℕ.
Set of Natural Numbers:
ℕ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...}
(continues infinitely)
Properties of Natural Numbers:
1. Closure Property – The sum or
product of two natural numbers is
always a natural number.
Example: 3 + 5 = 8, 2 × 4 = 8 (both
are natural numbers).
2. Associative Property – (a + b) + c = a +
(b + c) and (a × b) × c = a × (b × c).
Example: (2 + 3) + 4 = 2 + (3 + 4).
, 3. Commutative Property – a + b = b + a
and a × b = b × a.
Example: 4 + 6 = 6 + 4, 5 × 3 = 3 ×
5.
4. Identity Property –
Addition: a + 0 = a (0 is the
additive identity).
Multiplication: a × 1 = a (1 is the
multiplicative identity).
5. No Negative or Fractional Numbers
– Natural numbers do not include
negative numbers, fractions, or
decimals.
Types of Natural Numbers:
1. Even Natural Numbers – Numbers
divisible by 2: {2, 4, 6, 8, 10, ...}
2. Odd Natural Numbers – Numbers
not divisible by 2: {1, 3, 5, 7, 9, ...}
3. Prime Numbers – Numbers that
, have only two factors (1 and itself),
e.g., {2, 3, 5, 7, 11, 13, ...}.
4. Composite Numbers – Numbers
with more than two factors, e.g., {4,
6, 8, 9, 10, ...}.
