# Are constants and integers the same?

## Number sets: rational, irrational and real numbers

Math and numbers? It's somehow related. There are certain **Sets of numbers** in math. This text deals with three of these sets of numbers - with the sets of numbers of**rational numbers,** the**irrational numbers **and the**real numbers**. Here we will look at the definitions and discuss some examples.

If you want to learn more about the number set of natural numbers and whole numbers, you can continue learning in the learning text Number sets: natural and whole numbers.

### Rational (fractional) numbers

The **rational numbers** will too **fractional numbers** called, which will give you a little hint as to which numbers could be meant: It's the fractions.

The **rational****numbers** include in addition to the **whole****numbers** also fractions, such as $ \ frac {2} {3} \; or \; \ frac {3} {4} $. It doesn't matter whether the fraction is written as a fraction or whether it is a fraction **decimal number** trades, so the fraction was written out, for example $ 0.25 $. These numbers all belong to the rational numbers. The symbol of the rational numbers is the $ \ Large {ℚ} $.

##### rational numbers

The amount of **rational numbers** has the letter $ \ Large {ℚ} $. This is because the **rational numbers** which contain fractions and a **fracture** Yes one **division** is. The **Result** such a division is used in mathematics **quotient** called and this is how the letter Q can be explained.

**Rational numbers** are all **whole numbers** and additionally **all fractions**.

The **symbol** for the **rational numbers** is: $ \ Large {ℚ} $.

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### Irrational numbers

The **irrational numbers** are another crowd in math. The **irrational numbers** include by definition **Not** the**rational numbers**but the numbers that one **Not****as****fracture** can write. Have these numbers **infinite****lots****Decimal places** and therefore cannot be written as a fraction. Such numbers are above all **important constants**, how **pi**, or the **Euler's number**, but also the roots of numbers, $ \ Large {\ sqrt {2}} $. These numbers have an infinite number of decimal places and can therefore **Not****precisely determined** become. So if you are one of them **decimal number** you want to form the number **round**.

The **irrational numbers** are all values that **infinite****lots****Decimal places** to have. $ \ Large {\ sqrt {2}} $ or the well-known constant like $ \ Large {π \;} $ are examples of irrational numbers.

### Real numbers

The set of real numbers does not form a new group of numbers, but is a sum of the two sets mentioned above, the **rational** and the **irrational numbers**.

The **symbol** for the real numbers this is $ \ Large {ℝ} $

The **real numbers** are by definition all**irrational numbers** and **rational numbers**. It contains all the important sets of numbers that you need for school.

The symbol for the real numbers is the $ \ Large {ℝ} $.

**Order of the number sets:**

The **real****numbers** include the **irrational****numbers** and the **rational****numbers**. The **rational****numbers** include the **whole****numbers**. The **whole****numbers** include the **natural****numbers**.

$ \ Large {ℝ \ rightarrow ℚ \ rightarrow ℤ \ rightarrow ℕ} $

*Now you know more about rational numbers, irrational numbers and real numbers and have seen examples. To find out more about this topic, have a look at the Exercises! Good luck with it!*

**Your team of authors for mathematics: Simon Wirth and Fabian Serwitzki**

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### Test your knowledge!

Mark all the rational numbers.

Mark the correct statements.

Which statements are correct?

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