Closure property of multiplication: If p and q are natural/whole/rational/integer numbers then p × q is also a natural/whole/rational/integer number. Like in the above example, 4 and 9 are natural/whole/rational/integer numbers, so is their multiple (36).

Closure property of addition: The sum of two natural/whole/rational/integer numbers is also a natural/ whole number.

There are different sets of numbers. Two of them are rational and irrational numbers:

• Rational numbers: It is the set of numbers that can be expressed in the form of \({p \over q}\). For example \(2 \over 3\). A rational number can be classified into:
  • Natural Numbers: 1, 2, 3..... up to infinity are natural numbers.
  • Whole Numbers: 0, 1, 2, 3..... up to infinity are whole numbers.
  • Integers: 0, ±1, ±2, ±3...... up to ± infinity are integers.
• Irrational numbers: It is the set of numbers that can not be expressed in the form of \({p \over q}\). For example √3.
• Imaginary Numbers: Those numbers which are written in a + ib form, where i = √-1.

Hence, we conclude that all the above types of number follows closure property.