The irrational numbers

Irrational numbers are real numbers that cannot be expressed as a simple fraction of two integers. Their decimal expansion is non-repeating and never-ending, meaning the digits continue infinitely without following a predictable pattern. Examples include √2, π, and e. These numbers are essential in mathematics because they fill gaps in the number line that rational numbers (fractions) can't reach. While rational numbers can be written as fractions, irrational numbers require an infinite, non-repeating decimal representation, highlighting their unique, complex nature in the continuum of real numbers.