# Category:Irrational Numbers

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This category contains results about **Irrational Numbers**.

Definitions specific to this category can be found in Definitions/Irrational Numbers.

An **irrational number** is a real number which is not rational.

That is, an **irrational number** is one that can not be expressed in the form $\dfrac p q$ such that $p$ and $q$ are both integers.

The set of **irrational numbers** can therefore be expressed as $\R \setminus \Q$, where:

- $\R$ is the set of real numbers
- $\Q$ is the set of rational numbers
- $\setminus$ denotes set difference.

## Subcategories

This category has the following 4 subcategories, out of 4 total.

## Pages in category "Irrational Numbers"

The following 11 pages are in this category, out of 11 total.

### I

- Integer to Rational Power is Irrational iff not Integer or Reciprocal
- Intersection of Closures of Rationals and Irrationals is Reals
- Irrational Number divided by Rational Number is Irrational
- Irrational Number is Limit of Unique Simple Infinite Continued Fraction
- Irrational Numbers are Uncountably Infinite
- Irrational Numbers form G-Delta Set in Reals