Are All Natural Numbers Also Whole Numbers? | Set Facts

Questions about natural numbers and whole numbers pop up in school tests, entrance exams, and math puzzles. The terms sound almost the same, yet teachers sometimes treat them as different sets. When you keep the two definitions straight, related ideas like integers, fractions, and real numbers feel far less confusing. This article walks through the meaning of each set and shows clearly where they match and where they differ.

What Do We Mean By Natural And Whole Numbers?

In many school courses, natural numbers are the counting numbers you meet first: 1, 2, 3, 4, and so on. A common way to write this is N = {1, 2, 3, 4, …}. These values answer questions such as “How many books are on the shelf?” or “How many students are in the class?” Under this description, 0 does not join the list, and negative values stay out as well.

Whole numbers extend that list by adding 0 at the front. A frequently used description is W = {0, 1, 2, 3, 4, …}. You can think of whole numbers as the natural numbers plus 0, still with no negative values, decimals, or fractions. Many school resources, such as Britannica Kids’ overview of number systems, present counting numbers and whole numbers in exactly this way, with whole numbers starting at 0.

Some authors prefer a slightly different convention. They let the natural numbers start at 0, so N = {0, 1, 2, 3, …}. In that style, “natural” and “whole” describe the same set, just using two labels. Other authors keep natural numbers starting at 1 and reserve the word “whole” for the version that includes 0. The Math Is Fun natural number entry mentions both options and reminds readers to check which rule a book or course uses.

Common Number Sets And Their Typical Definitions

Set Name	Symbol	Definition Snapshot
Natural Numbers (starts at 1)	N	Counting numbers 1, 2, 3, 4, …; no zero, no negatives, no fractions.
Natural Numbers (includes 0)	N or ℕ0	0, 1, 2, 3, …; same terms as whole numbers in many texts.
Whole Numbers	W	0, 1, 2, 3, …; no negative values, no fractions, no decimals.
Integers	Z	…, −3, −2, −1, 0, 1, 2, 3, …; no fractional part.
Rational Numbers	Q	Numbers that can be written as a fraction of two integers with nonzero denominator.
Irrational Numbers		Numbers that cannot be written as a fraction of integers, such as √2 or π.
Real Numbers	R	All rational and irrational numbers on the number line.
Complex Numbers	C	Numbers of the form a + bi, where a and b are real and i² = −1.

This wider table shows that natural numbers and whole numbers fit inside a bigger family of sets. For most middle school and early high school courses, the only difference between those two sets is the presence or absence of 0.

Are All Natural Numbers Also Whole Numbers? In Everyday Math

Now we can tackle the exact question: are all natural numbers also whole numbers? Under the common school rule, the answer is yes. Every natural number belongs to the whole number set, because whole numbers include 0 and every positive counting number.

You can picture this as one set sitting inside another. Write N = {1, 2, 3, 4, …} and W = {0, 1, 2, 3, 4, …}. Every value in N also appears in W, so we say N is a subset of W and write N ⊂ W. The extra element in W is 0, which does not appear in N under this convention.

When a test asks, “Are all natural numbers also whole numbers?” the safest short answer in a course that defines N = {1, 2, 3, …} is “Yes.” A student can then add a short reason such as “Every natural number is a counting number greater than 0, and whole numbers contain 0 and all counting numbers.” That sentence already shows clear understanding during marking.

This direction still works even if you expand the natural number set later. If a course later adopts natural numbers starting at 0, the two sets merge, so the relationship “every natural number is whole” remains true. In that scenario, the two labels describe the same collection of values.

Are Natural Numbers Also Whole Numbers In Every Book?

Math is a global subject, and writers in different countries sometimes prefer different labels. A primary school book in one region might say that natural numbers start at 1, while a university text might write N = {0, 1, 2, 3, …}. Because of that, learners bump into lines such as “0 is not a natural number” in one place and “0 is a natural number” in another.

Thankfully, the underlying idea stays stable. The set with no negatives and no fractions that starts at 1 and continues upward is the same collection of values no matter which name you attach to it. The set that uses the same numbers but also includes 0 is also clear in practice. Symbols and labels may shift, yet the actual calculations you do with these values do not change.

When a new course begins, pay attention to the opening chapter or the teacher’s first notes on notation. Many authors now mention both conventions and state exactly which one they follow. Once that choice is clear, the question “are all natural numbers also whole numbers?” becomes a matter of translating that definition into set language.

Natural Numbers And Whole Numbers On The Number Line

A quick way to see the link between the two sets is to draw a horizontal number line. Mark 0 somewhere near the centre, then mark 1, 2, 3, 4, and so on to the right, with equal spacing. To the left of 0 you would see −1, −2, −3, and more negative values, although those do not belong to either the natural or the whole numbers in the usual school sense.

Placing Natural Numbers

Using the convention N = {1, 2, 3, …}, natural numbers sit at the tick marks to the right of 0 that have positive labels, starting at 1. There is no point at 0 in the natural number set under this rule. Every time you count objects, you move along these positive ticks: one, two, three, four, and so on.

Placing Whole Numbers

Whole numbers use those same positive ticks and also include the point at 0. When you say “there are zero apples in the bowl,” that 0 lives in the whole number set. In many number line diagrams in school workbooks, you will see an open circle or a filled dot at 0 when a teacher outlines the whole number set.

Seeing The Subset Relationship

On this number line picture, the natural numbers occupy every tick mark that the whole numbers use, except 0. That way of drawing the sets makes the subset idea feel natural: whole numbers run from 0 upward; natural numbers run from 1 upward; the second lies entirely inside the first.

How To Decide If A Number Is Natural Or Whole

Students often meet mixed sets of numbers in worksheets: fractions, decimals, square roots, integers, and more. A common task asks you to sort each value into groups such as “natural,” “whole,” “integer,” and “rational.” A short checklist keeps that sorting process calm and predictable.

Step 1: Check For Fractions Or Decimals

Look at the form of the number. If it appears as a decimal that does not end with .0, or as a clear fraction like 3/5, it does not belong to the natural or whole number sets. Both sets contain only numbers with no fractional part. Those values might still be rational, but they cannot be natural or whole.

Step 2: Check The Sign

If the number has a minus sign, it is not natural or whole. Negative numbers belong to the integer set but sit outside the two sets we are comparing here. So −4, −1, and −1000 are integers, yet they miss both the natural and whole lists.

Step 3: Decide Between Natural And Whole

Once you know the number has no fractional part and no minus sign, the only remaining question is whether 0 is allowed. Under the common school rule, 0 is whole but not natural; every positive count like 1, 2, 3, 4, and so on is both natural and whole. Under the alternative rule that includes 0 in N, any nonnegative number with no fractional part qualifies as both natural and whole.

Step 4: State The Convention You Use

Some exam questions give the convention in the problem statement. Others leave it to the course notes. If you write a short answer, a brief phrase such as “using N = {1, 2, 3, …}” next to your working removes any doubt. When answering “are all natural numbers also whole numbers?” you can then back up “Yes” with that shared convention.

Practice Questions With Answers

To lock in the idea, it helps to test a range of values. The table below assumes the convention N = {1, 2, 3, …} and W = {0, 1, 2, 3, …}. Under a different convention that includes 0 in N, the answers in the “Natural?” column would change for rows involving 0.

Classifying Numbers As Natural And Whole (N Starts At 1)

Number	Natural?	Whole?
7	Yes, 7 is a positive counting number.	Yes, every natural number is also whole.
0	No, 0 is not in N under this rule.	Yes, 0 is the first whole number.
−3	No, negative values are not natural.	No, negative values are not whole.
4.5	No, it has a fractional part.	No, whole numbers have no fractional part.
15	Yes, it is a positive integer.	Yes, it lies in both sets.
1/2	No, it is a proper fraction.	No, whole numbers exclude fractions.
100	Yes, it is a counting number.	Yes, every natural number is whole.
√2	No, it is not an integer.	No, it is not an integer.

Notice how the “Yes” answers in the “Natural?” column always match “Yes” answers in the “Whole?” column. That pairing reflects the idea behind the question “are all natural numbers also whole numbers?” Under the usual school convention, whenever a number passes the test for being natural, it automatically passes the test for being whole.

Why This Distinction Matters For Students

At first glance, the difference between natural and whole numbers feels tiny. Only 0 stands between them. Yet that single value affects how definitions line up later on. Prime numbers, factors, multiples, and various algebra topics all use natural or whole numbers as a starting point, so a clear picture of these sets keeps later topics cleaner.

Teachers also use the natural and whole number sets to build the ladder of number systems step by step. You start with counting numbers, add zero to form whole numbers, then bring in negatives to form integers. From there, fractions and decimals lead to rational numbers, and so on toward real and complex numbers. Each step reuses the previous one, so a clear sense of what belongs where saves effort when new terms arrive.

Finally, clear language around these sets pays off in written work. When you answer “Are all natural numbers also whole numbers?” on a quiz or exam, stating your convention and giving a short reason shows solid understanding. A marker can see that you know where 0 sits, how the sets nest inside each other, and how to move between verbal descriptions, set notation, and number line pictures. That level of clarity is exactly what most courses look for in early number theory and pre-algebra work.