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Math 101: What is a Whole Number?

Omkar Phatak Mar 2, 2019
If you are curious about whole numbers, this post will be an insightful read. In what follows, you will find a simple explanation of this fundamental concept in number theory.
Our journey into the world of mathematics starts with learning of numbers. There are various ways in which they can be classified according to different criteria. The most basic set of numbers are the natural and whole numbers.
A number is basically a symbol which represents a complete or indefinite quantity. It is a symbol which helps us express the quantity of objects, things, and magnitude of real world measurements. Most importantly, these quantifying symbols, which we call numbers, are the objects on which mathematical operations are carried out.
The prime operations of addition, subtraction, multiplication, and division in mathematics, when carried out on these numbers, help in establishing relations between different quantities. This part of mathematics which deals with numbers and operations carried out on them, is known as 'Arithmetic'.


Natural numbers are the set of numerals beginning from 1 and extending up to infinity. The set of natural numbers can be represented as (1, 2, 3, 4, 5, 6 . . . . ). Whole numbers are the set of natural numbers with zero added in. That is, the set begins from '0' and extends up to infinity.
So, the entire set of these numbers is - (0, 1 , 2, 3, 4. . . . ) extending till infinity. They are countably infinite. Another thing to note is that all whole numbers are essentially positive in value. These numbers are the set of all positive integers, with zero included.
The numbers are named as 'Whole', as they include no fractional or decimal part. To put it simply, they are 'exact' numbers, which are wholly rounded up with no associated decimal extension. All prime numbers are essentially whole numbers and are known to be their building blocks.
A consecutive whole number in a set is the one that precedes or succeeds another one. For example, '1, 2, 3' is a set of consecutive whole numbers. They are arranged successively and each number, when subtracted from its preceding number, yields the value 1.
Zero is the smallest whole number as there is no other number that is lesser than zero in that set. The largest one is positive infinity, which is a number that is greater than any other number you can imagine.
As discussed previously, the simplest way of identifying them is to check whether they have an extended 'decimal' part. If there isn't, that means the number is 'wholesome', with no additional fractional part in it.