What is the set of real numbers

Real numbers

The so-called real numbers are covered in this article. This means all numbers that belong to the rational and irrational numbers. What exactly this is all about, we explain in the following article.


First, a quick note: this article goes into great detail about real numbers. For all those who just need brief information on this term in mathematics, our summary in the article Types of Numbers is sufficient.

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Properties of real numbers

The set of real numbers is the union of the rational numbers and the irrational numbers. For this reason, it is useful and important to know what is behind these two types of numbers.

A rational number - often also called a fractional number - is understood to mean all numbers that can be represented as a fraction. Example: 1/2; 3/4; 4/5 etc .. The numbers thus have the form z / n, i.e. numerator by denominator, as you hopefully already know from fractions. In contrast to the decimal fractions, these fractions are often referred to as ordinary or common fractions.

Rational numbers can be represented as a fraction, irrational numbers cannot. For example, if you take the root of the number 2, you get about 1.4142. However, this number is imprecise, because the root of 2 has an infinite number of places after the decimal point. This also applies to the circle number π (pronounced: pi), for which the value 3.14 is usually used as an approximation in schools. In practice you break off after a certain place after the comma and thus get a finite decimal number (point number).

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