Real number that cannot be written in the form of the ratio \(\frac {a}{b}\) where \(a\) and \(b\) are integers and \(b\) ≠ 0.
Symbols
The symbol \(\mathbb{Q’}\) represents the set of irrational numbers and is read as “Q prime”.
The symbol \(\mathbb{Q}\) represents the set of rational numbers.
Combining rational and irrational numbers gives the set of real numbers: \(\mathbb{Q}\) U \(\mathbb{Q’}\) = \(\mathbb{R}\).
Examples
The numbers \(\sqrt{5}\), \(\sqrt{11}\), \(\dfrac{\sqrt{5}}{7}\), π and e are irrational numbers.
- \(\sqrt{5}\) = 2.236 067 …
- \(\sqrt{11}\) = 3.316 624 …
- \(\dfrac{\sqrt{5}}{7}\) = 0.319 438 …
- π = 3.141 592 …
- e = 2. 718 281 …