What type of numbers cannot be expressed as fractions or decimals due to their infinite and non-repeating nature?

Irrational numbers are defined as numbers that cannot be expressed as a fraction, where both the numerator and the denominator are integers and the denominator is not zero. They have decimal representations that are both infinite and non-repeating. Classic examples of irrational numbers include the square root of 2 and pi (π). Unlike rational numbers, which can be expressed in a simple fractional form, irrational numbers do not fit into such categories, as their decimal expansions continue indefinitely without forming a repeating pattern. Therefore, the identification of irrational numbers aligns perfectly with the characteristics outlined in the question.