The major Properties of Integers are: Closure Property. Associative Property. Commutative Property. Distributive Property. Additive Inverse Property. Multiplicative Inverse Property. Identity Property.
Closure property states that any operation conducted on elements within a set gives a result which is within the same set of elements. Integers are either positive, negative or zero. They are whole and not fractional. Integers are closed under addition.
The closure property of the division tells that the result of the division of two whole numbers is not always a whole number. Whole numbers are not closed under division i.e., a ÷ b is not always a whole number. From the property, we have, 14 ÷ 7 = 2 (whole number) but 7 ÷ 14 = ½ (not a whole number).
If the division of two numbers from a set always produces a number in the set, we have closure under division. The set of whole numbers are not closed under division, and the set of integers are not closed under division because they both produce fractions.
The division property of equality means when both sides of an equation are divided by the same number, the equation will remain true. The divisor cannot be zero, and must be the same on both sides of the equal sign in order for this property to hold true.
Closure property formula states that, for two numbers a, and b from set N (natural numbers) then, a + b ∈ ℕ a × b ∈ ℕ a - b ∉ ℕ
A natural number is closed under addition and multiplication. This means that adding or multiplying two natural numbers results in a natural number. However, for subtraction and division, natural numbers do not follow closure property. When a and b are two natural numbers, a+b is also a natural number.
Closure property holds for addition and multiplication of whole numbers. Closure property of whole numbers under addition: The sum of any two whole numbers will always be a whole number, i.e. if a and b are any two whole numbers, a + b will be a whole number. Example: 12 + 0 = 12. 9 + 7 = 16.
Do you know why division is not under closure property? The division is not under closure property because division by zero is not defined. We can also say that except '0' all numbers are closed under division.
The sum of any two integers will always be an integer, i.e. if a and b are any two integers, a + b will be an integer. Closure property of integers under subtraction: The difference between any two integers will always be an integer, i.e. if a and b are any two integers, a – b will be an integer.