Operations On Whole Numbers

What are whole numbers?

A whole number is the set of all-natural numbers and numbers that contain 0. These are some real numbers that do not contain fractions, decimals, or negative numbers. Counts are also considered whole numbers.

A natural number is the set of counts starting at 1. Natural numbers and zero (0), on the other hand, form a set called a whole number. However, zero is an undefined ID that represents a null set or does not have any results. Simply put, a whole number is a set of numbers that do not contain fractions, decimals, or even negative integers. This is a collection of positive integers and zeros. Alternatively, an integer can be said to be a set of non-negative integers. The main difference between natural and whole numbers is the presence of zeros in the set of whole numbers.

A whole number is a set of natural numbers but with the number 0. The set of math integers is given as {0, 1, 2, 3, …}, which is indicated by the symbol W. 

 W = {0, 1, 2, 3, 4, …}

Is every natural number a whole number?

Yes, all the natural numbers are whole numbers, but all the whole numbers are not natural numbers, and in fact, every counting number, positive integers which include zero are whole numbers, and all the whole numbers are real numbers.

The set of whole numbers starts from zero, whereas the set of natural numbers starts from 1. So, the smallest whole number is 0, and the smallest natural number is 1; in fact, every natural number is a whole number, whereas every whole number is a natural number except zero (0). 

Natural numbers are also called a subset of whole numbers.

Which is the smallest whole number?

Zero (0) is the smallest whole number. The concept of zero was found by the Hindu astronomer known as mathematician Brahmagupta in 628. In simple terms, on the number line, zero always lies between the positive and negative numbers. Null has no value, but then people use zero as a placeholder. Therefore, zero is not a positive number as well as not a negative number. 

If we talk about which is the largest whole number, then there is none. Except zero with every whole number, there is a successor (a number that comes before a number) and a predecessor (a number that comes after a number). If there is a decimal number or a fraction, then it will lie between two whole numbers but will not be called whole numbers.

What are the properties of a whole number?

The properties of a whole number are:

• Closure property: it states that when we add or multiply two whole numbers, then the outcome will always be a whole number. For example, if we add 1 and 2, we will get 1+2 = 3, which is a whole number, and if we multiply 1 and 2, then we will get 2, which is also a whole number.  

But in the case of subtraction and division, it is not applicable.

• Associative property: it states that if we do sum or find a product of any three whole numbers, it will always remain the same no matter how the numbers are grouped together.

For example, 1+2+3 = 3+1+2

And,

1×2×3 = 3×1×2

This property is not applicable for subtraction and division because the arrangement of numbers can create a major difference.

Conclusion:

whole numbers such as 0, 1, and 2 are components for understanding more complex number identifiers such as real, rational, and irrational numbers. Rounding to the nearest integer also helps to perform calculations and mental arithmetic faster. Whole numbers are always positive numbers that do not contain a fractional or a decimal part. For example, the numbers 0,1,2,3,4,5 are all whole numbers, but the numbers like -3, -4, -5, -6, or 3 ½ are not called whole numbers. Whole numbers are up to infinity, and the smallest whole number is zero.