Are constants and integers the same?

Number sets: rational, irrational and real numbers

Mathematics> Number theory and arithmetic laws

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 ofrational numbers, theirrational numbers and thereal numbers. Here we will look at the definitions and discuss some examples.

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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 rationalnumbers include in addition to the wholenumbers 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} $.

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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.

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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 therational numbersbut the numbers that one Notasfracture can write. Have these numbers infinitelotsDecimal 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 Notprecisely determined become. So if you are one of them decimal number you want to form the number round.

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The irrational numbers are all values ​​that infinitelotsDecimal 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} $

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The real numbers are by definition allirrational 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 realnumbers include the irrationalnumbers and the rationalnumbers. The rationalnumbers include the wholenumbers. The wholenumbers include the naturalnumbers.

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

Numbers in comparison: overview

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 theExercises! Good luck with it!

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