# Are natural numbers negative

## Number sets: natural and whole numbers

Mathematics> Number theory and arithmetic laws

In the mathematics there are different groups of numbers including thenatural, therationalor also theirrationalnumbers. But what exactly in these Sets of numbers is not always telling you the name. Here we will explain the set of natural and whole numbers to you in more detail.

### 4 facts about natural and whole numbers

We have already listed the most important things about the number set of natural and whole numbers:

1. All positive numbers up to infinity that have no decimal place belong to the natural number set \$ ℕ \$.
2. The number \$ 0 \$ is usually not assigned to the set of natural numbers.
3. The whole set of numbers \$ ℤ \$ includes all numbers that have no decimal place: the natural numbers, all negative numbers and the number \$ 0 \$.
4. The number \$ 0 \$ is assigned to the set of integers.

Isn't everything clear yet? You have now received a small overview of natural and whole numbers. We would now like to explain everything to you in a little more detail, so that you become fit in this topic.

### Natural numbers

The natural number set is the simplest set of numbers, because every number you get to know at the beginning of your math class is a natural number. These also have one specific symbolso that you can recognize them.

The natural numbers are all numbers from 1 to infinity \$ (\ infty) \$. In addition, they have no decimal places. The Notation is:

\$ \ Large {ℕ = (1,2,3,4, ..., \ infty)} \$, or

\$ \ Large {ℕ _ {+} = (1,2,3,4, ..., \ infty)} \$  • Over 700 learning texts & videos
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### Natural numbers and the zero

So the natural numbers are allpositivenumbersthat have no decimal place. But what about the number \$ 0 \$? This has none Decimal place and could also be in the quantitythenaturalnumbers fit.

Usually the \$ 0 \$ is not going to be the natural numbers counted. However, if it is added to it, it must be evident and it is then written as follows:

The natural numbers, including the \$ 0 \$, are written as follows:

\$ \ Large {ℕ_ {0} = (1,2,3,4, ..., \ infty)} \$

### Whole numbers Number line with whole numbers. The spaces between the numbers are not whole numbers.

The wholenumbers expand the naturalnumbers to the negativenumbers. So the numbers \$ -1, -2, -3, ... \$ are part of the whole numbers.

The whole numbers include all numbers that are none Decimal place to have. They include the numbers from \$ - \ infty \; to + \ infty \$, thus always the number \$ 0 \$.

The symbol for the whole numbers this is \$ \ Large {ℤ} \$

The Notation is: \$ \ Large {ℤ = (..., -3, -2, -1, 0, 1, 2, 3, ...)} \$

### Whole Numbers - Opposite Numbers

The concept of opposite numbers describes the numbers that make up the same distance to have \$ 0 \$, i.e. the numbers \$ -8 \; \$ and \$ 8 \; \$ or \$ -4 \; \$ and \$ 4 \; \$. The distance between the two numbers is therefore exactly \$ 2 \ cdot \; "number" \$, in the first two examples this is \$ 2 \ cdot \; 8 = 16 \$ and for \$ 2 \ cdot \; 4 = \$ 8.

To find out more about this topic, have a look at the Exercises to whole numbers and other numbers! Your team of authors for mathematics: Simon Wirth and Fabian Serwitzki

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