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# Natural Number|Definition & Meaning

## Definition

An **integer** greater than 0 is **called** a natural number. **Natural** numbers start at 1 and go up to **infinity,** like 1, 2, 3, 4, 5, etc.

A **natural** number is a number that is **common** and obvious in nature. It is a whole, **positive** number. The definition of **natural numbers** is exclusive of zero because counting **starts** with** 1**. This is how they look like in **set** notation and on a **number** line 1, 2, 3, 4, . . ., $\infty$

## What Are Natural Numbers?

The **numbers** you use for **counting** are natural numbers, for example, its **definition** says that it includes all the **positive numbers** from 1 to infinity. These **numbers** are the fundamental bases of the number system and they **occur** in nature. Therefore, we see **examples** of natural numbers **everywhere** around us in the **world.**

**Natural** numbers are **exclusive** of fractions, **decimals, zero,** or **negative** values. They are **tallies** of occurrences, but they **also** order **things** on a number line. The **smallest** natural **number** is 1. The **natural** numbers set starts with 1 as its **lowest** or starting value, and 1 is also the smallest possible **difference** between any two given numbers. For **example,** the closest numbers to** 5** are** 4** and 6, one less and one more, respectively.

**Natural numbers** are countably infinite which **means** that you can count all the possible values, but they **extend** to **infinity,** just as the right arrow on the number line of **natural** numbers indicates.

### Natural Number Examples

By **definition,** natural numbers are used in your daily lives whenever you start to count something. **Natural** numbers quantify and order the primary things in your life.

**Natural numbers** help you to count objects. For **example,** our office has two cafeterias. They also help you order **things** by putting them on the **number line.** For example, you can order a country’s population by the counts of the people living there.

The following are examples of natural numbers:

- The
**number**of sandwiches you ate today. - The number of
**steps**you**walked**today. - Comparing to see whether
**Drake**or Bob walks more steps. - The
**number**of students in your**class.**

## Comparison With Other Types of Numbers

Natural **numbers** are also sometimes called **counting** numbers and ordinal numbers. They are discrete numbers that perform in a contrast to continuous numbers. **Discrete** numbers are counted but continuous numbers are **measured.** Natural numbers are the basic foundation on which other number types build by **extension.**

### Difference Between Natural Numbers and Whole Numbers

Natural **numbers** are generally defined as primary **counting** numbers. The **natural** numbers in set notation look like: {1, 2, 3, 4, 5, …..}. The letter that **represents** the Natural number is “N.” In natural numbers, the **counting** starts from the **number** 1. All natural numbers are whole numbers.

**Whole numbers** are defined as a set of **natural numbers** and an **additional** zero. The **whole numbers** in set notation look like: {0,1, 2, 3, 4, 5, ….}. The letter “**W**” represents the Whole numbers. With **whole numbers,** the Counting number begins from 0. It is said that all whole numbers are not **natural** numbers.

Whole **numbers** include all counting numbers or **natural numbers** and they add the zero, as shown in the **Venn diagram.** Whole numbers add zero. **Zero** is more of an advanced concept that **mathematicians** added to number **theory** relatively **later.**

### Difference Between Natural Numbers and Integers

Integers **include** all natural numbers, their negative **values,** and zero.

The sets below **summarize** and explain the various types of discrete **numbers:**

Natural Numbers = {1, 2, 3, 4, …, $\infty$}

Whole Numbers = {0, 1, 2, 3, 4, …, $\infty$}

Integers = {$- \infty$ , . . ., -4, -3, -2, -1, 0, 1, 2, 3, 4, …, $\infty$}

## Usage of Natural Numbers

**Natural** numbers are also **known** as **“counting numbers”** because they are in counting. For **example,** if you are counting something, you would use natural **numbers** (usually starting with 1). When **writing** down, natural numbers do not **include** decimal points (since they are integers), but the **larger** natural numbers **might** include commas, e.g. **20,000** and **127,567,100**. Natural **numbers** can never include a **minus** symbol (-) because they are **always** positive.

In **computer** science, natural **numbers** are usually used in increasing values. For **example,** in a loop, the counter will usually be **increased** by one with each iteration of the loop. Once the counter reaches the **limit** (e.g., 5 in for **(i=1; i<5; i++)**), the loop ends and the code after the loop is **executed.**

## Properties of Natural Numbers

### Addition Property of Natural Numbers

The **addition** of two natural **numbers** results in a natural number only. Because **Natural** numbers are greater than 0 and the sum of anything greater than 0 will be **greater** than **zero.** For example:

**30+43 = 73**

When a **natural** number is **added** to a whole number the **result** will a natural **number.** For example:

**0+30 = 30**

### Subtraction Property of Natural Numbers

When two **Natural** Numbers are **Subtracted** the result does not necessarily be a natural number. The **reason** is explained in the below **examples.**

**11 – 6 = 5**

In the above **example** the result is 5 which is a **natural** number, now look at the example **below,**

**6 – 11 = -5**

The result is **-5** which is not a **natural** number so in this case, the **subtraction** of two natural numbers is not a **natural** number.

### Multiplication Property of Natural Numbers

When a **natural** number is multiplied by the **natural** number the result will also be a **natural** number **because** when two numbers are multiplied and both are **greater** than 1 the result is **also** greater than 1. For **example:**

**5 \times 4 = 20**

Which is **a natural** number.

### Division Property for Natural Numbers

**Natural numbers** do not hold the **division** property because division can **produce** numbers in decimals that are not **natural** numbers. For **example:**

**12/3 = 4**

A **result** is a natural number in this **case** but in the below case:

**15/2 = 7.5**

Which is not a **natural** number.

## Solved Example of Identifying Natural Numbers

From the series of numbers given in the figure below, find **natural** numbers.

### Solution

Natural **Numbers** from the **above-given** list are **45, 7, and 80**.

*All images/mathematical drawings were created with GeoGebra.*