A Whole Number A Whole Number We have studied about the counting numbers. The numbers used for counting are called natural numbers. 1, 2, 3, 4, ------- up to infinite are all natural numbers. If we add 0 to the set of natural numbers, it becomes the set of whole numbers. This means, the set of whole numbers is 0, 1, 2 , 3, ………. up to infinite are called whole numbers. A set of whole numbers is used for various measurements may it be distance, speed, weight , volume or any other measurement. We observe that every natural number has a successor, which we can get by adding 1 to any given whole number. For instance, successor of 245 is 245 + 1 = 246, successor of 890 is 890 + 1 = 891. Similarly we see that every whole number except 0 has a predecessor, which we can get by subtracting 1 from the given number. As we can see, the predecessor of 45 is 45 – 1 = 44, predecessor of 900 is 900 – 1 = 899. Here are some of the properties of whole numbers : 1. Closure Property: If a, b are any whole numbers, then a+ b is also a whole number. We say that whole numbers satisfy the closure property of addition, 2. Similarly according to the closure property of subtraction, if a , b are any two whole numbers such that a > b, then a – b is also a whole number. E.g. if a = 9 and b = 4 , then a – b =9 – 4 = 5. Here we find that a - b is also a whole number. Know More About :- Kite in Geometry
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3. Closure Property of multiplication also holds true, thus we can say that if a and b are whole numbers, then a * b is also a whole number. E.g. if a = 3 and b = 5 then a * b = 3 * 5 = 15 is also a whole number. 4. Closure property does not always holds true for the division operation, which means that if a, b are whole numbers, then a / b is not necessary a whole number. 5. Commutative Property of whole numbers holds true of addition and multiplication but not for subtraction and division : It says that if a and b are any two whole numbers then a + b = b + a and a * b = b * a. But we also have a – b ≠ b – a and a / b ≠ b /a 6. Additive Identity and Multiplicative Identity : If a is any whole number, then there exists a whole number 0, such that a + 0 = a . Also there exists a whole number 1, such that a * 1 = a. So we can say that 0 is the additive identity and 1 is the multiplicative identity. So we can say that if any number is added to 0, the result is the original number, and if 1 is multiplied to any number, the result is the original number.
Read More About :- Properties of Rational Numbers
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