Natural Numbers

Number classes

Natural numbers can also be part of other number classes, and the diagram below shows how they are all related;

Number Classes, Thomas-Gay - StudySmarter Originals

Properties of natural numbers

Natural numbers have four different properties;

• Closure property – this means that when two or more natural numbers are multiplied or added together, it will result in a natural number. For example, $2+2=4$ or $3\times 2=6$.

• Associative property – suggests that when three natural numbers are added or multiplied together, it will result in the same answer no matter how they are grouped. For example, 3 + (2 + 5) = 10 and (3 + 2) + 5 = 10. This also works when they are multiplied, $3\times (2\times 5)=30$ and $(3\times 2)\times 5=30$.

• Commutative property – this property says that when two natural numbers are multiplied or added together, they will result in the same answer no matter their order. For example, 4 + 8 = 12 and 8 + 4 = 12. This also works when they are multiplied, $4\times 8=32$ and $8\times 4=32$.

• Distributive property – when three natural numbers are being multiplied using brackets, you can also do this by multiplying the numbers separately. For example, 5 (2 + 3) = 25 and $5\times 2\hspace{0.17em}+\hspace{0.17em}5\times 3=25$.

What is the natural numbers symbol?

A set of natural numbers is often represented by the symbol $\mathrm{\mathbb{N}}$.

How to find the sum of natural numbers

The list of natural numbers creates an arithmetic sequence. There is a formula that you can use to help you find the sum of a sequence of natural numbers:

$\sum _1^n=\frac{\left(n\right(n+1\left)\right)}{2}$

In the above formula, n represents the number of terms. The sequence will start with 1. It is also important to note that the sum of all natural numbers is infinity.

Learn more about arithmetic Sequences and Series.