What Is a Whole Number but Not a Natural Number? | Zero

A whole number that isn’t a natural number is most often 0, since many classes treat natural numbers as starting at 1.

You’ll run into this question the moment you compare two textbooks that “agree on everything” and still label 0 differently. One calls 0 natural. Another keeps natural numbers for counting: 1, 2, 3, and up. Both can be used correctly, as long as the class sticks to one meaning.

So what’s the clean answer? In the common school setup, whole numbers are 0, 1, 2, 3, … and natural numbers are 1, 2, 3, … . Under that setup, 0 is a whole number but not a natural number.

What People Mean By Natural And Whole Numbers

Math words can be slippery when they come from everyday language. “Natural” sounds like it should be the most basic set. “Whole” sounds like it should mean “no fractions.” Those instincts aren’t wrong, but classrooms and books don’t always line up.

Natural Numbers As Counting Numbers

In many school courses, natural numbers match counting. You start at 1 because you start counting one thing, then two things, then three. Under this meaning, the set is {1, 2, 3, …}.

That choice also fits how counting is used in speech: “I have one pen” is the first count. “I have zero pens” is a real statement, but it’s not a count that begins the same way.

Whole Numbers As Counting With Zero Included

Whole numbers often keep the “no fractions” idea and also keep the “no negatives” rule. So you get {0, 1, 2, 3, …}. Zero sits at the start as the number that represents none.

This is why many elementary lessons say: whole numbers are the counting numbers plus 0. Khan Academy teaches whole numbers this way, with 0 included and negatives left out.

Why Some Sources Put 0 In The Natural Numbers

In higher math, you’ll see natural numbers written as 0, 1, 2, 3, … in plenty of places. That choice can make formulas cleaner, since 0 behaves nicely in many rules. It also matches how some standards and authors treat sequences and set notation.

This isn’t a “right vs wrong” battle. It’s a convention choice. The catch is that you must know which choice your class, worksheet, or test is using before you answer “Is 0 natural?”

Whole Numbers That Aren’t Natural Numbers In Many Classes

If your course uses:

• Natural numbers: {1, 2, 3, …}
• Whole numbers: {0, 1, 2, 3, …}

then the whole-number-but-not-natural-number is:

• 0

That’s the main “edge case” students get quizzed on. It’s also the one that shows whether you noticed the definition your class picked.

Why Zero Is The Only Answer Under The School Definition

Under the school definition, every whole number except 0 is also a natural number. Whole numbers and natural numbers match from 1 upward. So there’s only one number left over: 0.

It can feel too simple, which is why teachers like it as a check. If you can explain why 0 lands where it lands, you’ve got the sets straight.

Where Confusion Starts

Confusion often starts when someone hears “whole numbers are numbers without decimals.” That’s close, but it’s missing a piece. Numbers without decimals include negative integers too: −3, −2, −1, 0, 1, 2, 3, … . That larger set is called the integers.

So if you hear “whole means no decimals,” pause and ask: are negatives allowed? If negatives are allowed, the speaker is really talking about integers, not whole numbers in the school sense.

How To Tell Which Definition Your Class Is Using

You don’t need a long debate. You need a quick check that’s easy to repeat on homework nights.

Check The First Example On The Page

Look for a list like “natural numbers: 1, 2, 3, …” or “natural numbers: 0, 1, 2, …”. Many authors show the first few terms early. That single line answers your question right away.

Watch The Notation Around N

Some materials use symbols to remove doubt:

• N may mean naturals, with the starting point defined nearby.
• N₀ often means naturals that include 0.
• N₁ can be used for naturals that start at 1.

Not every class uses these, but when they appear, they’re a gift. You can stop guessing.

See How They Treat “Counting”

If a lesson says “counting numbers” and lists 1, 2, 3, … then it’s placing counting at 1. Many school texts then label those counting numbers as natural numbers, and label 0 plus the counting numbers as whole numbers.

Use A One-Line Test Question

Ask yourself: “Is 0 natural in this course?” If an example or practice set puts 0 under natural numbers, then your course is using the 0-included meaning. If 0 appears only under whole numbers or integers, then your course is using the start-at-1 meaning.

Britannica’s entry on natural numbers notes this split plainly: natural numbers are the positive integers and sometimes zero. That “sometimes” is the whole story.

When you need a dependable classroom-friendly definition of whole numbers with 0 included, Khan Academy’s explanation is clear and matches what most school worksheets expect: Khan Academy’s “Whole numbers & integers” lesson.

What Changes When Natural Numbers Start At 0

If your class puts 0 in the natural numbers, then the question “a whole number but not a natural number” has a different answer: none. Whole numbers and natural numbers become the same set in that setup.

Why Some Courses Prefer 0 In Naturals

Starting at 0 can make counting steps in formulas feel smoother. A sequence can begin with a “zeroth term.” Indexing in computer science often starts at 0. Many proofs and definitions also use 0 as a clean starting point.

When that’s the plan, teachers often stop using “whole numbers” at all, since “natural numbers” already covers 0, 1, 2, 3, … .

Why Some Courses Keep Naturals Starting At 1

Starting at 1 keeps “natural” tied to counting objects in the simplest way. It also keeps a tidy ladder of sets that students learn early:

• Natural numbers: 1, 2, 3, …
• Whole numbers: 0, 1, 2, 3, …
• Integers: …, −2, −1, 0, 1, 2, …

That ladder is easy to memorize and easy to test.

Common Definitions Side By Side

Since different sources use different starts, it helps to keep a quick comparison on hand. This table is a “spot the definition” tool. Match your class to a row, then you’ll know where 0 lands.

Where You See It	Whole Numbers	Natural Numbers
Elementary worksheets (common)	0, 1, 2, 3, …	1, 2, 3, …
K-8 “counting numbers” lessons	Counting numbers + 0	Counting numbers (start at 1)
Some pre-algebra texts	0, 1, 2, 3, …	1, 2, 3, … (called “naturals”)
Discrete math notes (common)	Often not used	0, 1, 2, 3, …
Computer science indexing	Rare term	0-based counts used in arrays
Number theory books	Rare term	Either start is defined near the start
Contest math rules	Defined per contest	Defined per contest
Standards and formal notation	May be avoided for clarity	N, N0, N1 used to spell it out

Zero’s Job In The Number System

Even if your class doesn’t call 0 “natural,” it still behaves like a first-class citizen in arithmetic. Knowing what 0 does makes the definitions feel less like a naming game.

Zero As The Additive Identity

Add 0 to any integer and you stay where you started: 7 + 0 = 7, and −4 + 0 = −4. That’s why 0 is called the additive identity. It’s the “do nothing” add for addition.

Zero As A Placeholder

In base-10 writing, 0 also holds a place. The difference between 51 and 501 is not a tiny detail. The 0 keeps the 5 in the hundreds place and leaves the tens place empty.

Zero And Counting Real Things

Zero counts “none.” If you have 0 coins, that’s a count. Still, many early math sequences for counting begin at 1 since they’re built around “one item” as the first step. That’s why the natural-number definition splits in classrooms.

Spotting Whole, Natural, Integer, And Beyond

Students often mix up sets because they’re taught close together. Here’s a clean way to keep them apart without memorizing a wall of terms.

Whole Numbers Vs Integers

Whole numbers stop at 0 on the left. Integers keep going: …, −3, −2, −1, 0, 1, 2, 3, … . If a question uses a negative value, it’s already outside whole numbers.

Whole Numbers Vs Rational Numbers

Rational numbers include fractions and terminating or repeating decimals, like 3/4, 0.25, and 2.6̅. Whole numbers are just the nonnegative integers. So every whole number is rational, but not the other way around.

Natural Numbers Vs Whole Numbers

If your course starts naturals at 1, then naturals are whole numbers without 0. If your course starts naturals at 0, then naturals and whole numbers match.

Classification Practice With A Clear Rule

Use this table with the common school meanings: whole numbers start at 0, natural numbers start at 1. If your class uses a different start for naturals, adjust the “Natural?” column for 0.

Number	Whole?	Natural? (Start At 1)
0	Yes	No
1	Yes	Yes
8	Yes	Yes
−2	No	No
3/5	No	No
12.0	Yes (same value as 12)	Yes
2.7	No	No

Answers Teachers Like To See

On assignments, teachers often want two parts: the number and the reason. A short reason keeps you safe if the worksheet uses a definition you didn’t expect.

Answer Template For The Common School Setup

• Answer: 0
• Reason: whole numbers include 0, while natural numbers start at 1 in this class.

Answer Template When Naturals Include 0

• Answer: none
• Reason: natural numbers and whole numbers are the same set here: 0, 1, 2, 3, … .

Small Checks That Prevent Lost Points

When a test mixes vocabulary from different chapters, tiny wording cues can save you.

Look For “Positive”

If a definition says “positive integers,” it excludes 0. That points to naturals starting at 1. If it says “nonnegative integers,” it includes 0. That points to whole numbers, or naturals that include 0.

Read The First Worked Solution

If a worked solution labels 0 as natural, follow that. If it labels 0 as whole but not natural, follow that. Matching the source beats guessing.

Write The Set In The Margin

On paper tests, jot “W: 0,1,2…” and “N: 1,2,3…” in the margin when that’s the class rule. It takes two seconds and keeps your answers consistent across the page.

If you want one outside source that states the natural-number split plainly, Britannica says natural numbers are the positive integers and sometimes zero: Britannica’s “Natural number” definition.