Types of Numbers: Whole Numbers

Quantifying things is a crucial part of our daily life. We have to count everything around us almost every day. Since we deal with numbers very frequently, it’s essential that we know the types of numbers that exist. The most common types of numbers discussed in mathematics are natural numbers and whole numbers. While they are not so much different from each other, that little difference matters a lot during calculations. 

Whole Numbers Definition:

The whole number term in mathematics has been ambiguously associated with it. To could either refer to a set consisting of natural numbers along with 0 or a set like {…, −2, −1, 0, 1, 2, …} where no fractions can exist.

However, according to the formal definition and context in which we’re studying, a whole number can be defined as a whole number that is simply any number that does not consist of a fractional or decimal part. It’s only made of whole parts, that’s why it’s named as a whole number.

What are Whole Numbers?

Now that we’ve covered the legal definition part let’s see what whole numbers are and which number could be termed a whole number.

The whole number set is a collection of all positive integers and 0. It is a number without any fraction.

Representation:

A whole number or a set of whole numbers can be represented with the letter “W,” where the “W” stands for the whole. It could be small as well as capital.

Subset Relation:

Since there are so many ways in which numbers are classified, a particular type could be a subset or superset of some other type.

Following that, the natural number subset is the subset of the whole number set. This means all natural numbers are whole numbers as well. But not all whole numbers are natural numbers. For example, 0.

However, the whole number set is a subset as well. All whole numbers are rational numbers. And given that all rational numbers are real numbers, all whole numbers are real numbers too. So, to conclude, a whole number set is:

Superset of the following sets are:

• Natural number set

A subset of the following sets:

• Rational number set
• Real number set

The way to determine whether a given number is a whole number. We should be considering the following three factors while analyzing whether a given number can be called a whole number.

• A whole number should be a positive and not a negative number or integer, also known as a minus number. This means the value of a whole number should be 0 or higher than that.

For example, 0, 1, 2, and 3 can all be called whole numbers. However, -1, -2, and -3 won’t be called whole numbers.

• A whole number cannot consist of any fractional element, which would mean numbers such as 1 ½, 3 ¼, and 7 ⅚ are not whole numbers, but 1, 3, and 7 are.
• A whole number cannot have any decimal element. So, the numbers such as 1.7, 3.9, and 19.234 are not whole numbers, but 1, 3, and 19 are whole numbers.

Rounding to the Nearest Whole Number

Sometimes, when we need to provide an approximate quantity of something, we are expected to provide that in the form of a whole number. This means we have to find the whole number which is most similar to the value of a given non-whole number.

• 13.37 will be rounded up to 13
• 1.12 will be rounded unto 1 as it is a nearest whole number
• The nearest whole number to 2 ¼ is 2, so it gets round up to 2
• 67 ⅚ will be rounded up to 68

Some Interesting Facts about Whole Numbers

• There is no ‘largest’ whole number as whole numbers stretch up to infinity. Infinity is never-ending.
• Except for 0, every whole number has a number that comes before or immediate predecessor.
• A decimal, fraction, or a number lies between two whole numbers.

Also, there are a few other things about the whole number that would be considered remarkable. The addition and multiplication of two whole numbers is always a whole number.

At the same time, the subtraction or division between two whole numbers might not always result in a whole number. All the whole numbers lie on the right side of the number line. Except for the number 0, which is considered as the center of the number line.

Conclusion

A whole number is a number that does not consist of a fractional part. It’s only made up of the whole part. A whole number is a positive integer or 0. It is a superset of the natural number set and the subset of rational and real numbers.

We can identify whether a certain number is whole by making sure it doesn’t have a decimal or fractional part and also that it’s not a negative number. There is no largest whole number as whole numbers stretch up to infinity. Most of the whole numbers lie to the right of the number line except 0, in the middle. So, from this article, we learn about the whole number and whole number definition.