Irrational numbers

Irrational numbers are numbers with an infinite non-recurring decimal expansion. They include some well-known constants such as π or Euler’s number e.

Definition

Irrational numbers are the real numbers that cannot be written in the form of a fraction, that is, as the quotient of two integers. Written as a decimal, they have an infinite decimal expansion with no recurring digits.

The irrational numbers include π and, for example, $\sqrt{2}$.

Properties

1. The irrational numbers form an infinite uncountable set.

What we do not know

There are some open questions about irrational numbers. It is not known whether the results of these operations are irrational numbers or rational numbers.

$$\pi +e,\pi -e,\pi \cdot e,\pi /e,2^e,{\pi }^e,{\pi }^{\sqrt{2}},\ln \pi$$

Links

• Be sure to read the story of where Euler’s number came from
• Wikipedia