Which set of numbers is classified as an irrational number?

The classification of an irrational number is based on its inability to be expressed as a simple fraction or a ratio of two integers. An irrational number cannot be precisely represented as a terminating or repeating decimal.

The set consisting of Pi and non-terminating decimals perfectly exemplifies irrational numbers. Pi is a well-known example of an irrational number since its decimal representation goes on infinitely without repeating. Non-terminating decimals, such as the square root of any prime number or numbers like e (the base of natural logarithms), also fit this category as they do not settle into a repeating pattern.

Meanwhile, the other sets mentioned consist of numbers that can be expressed as rational numbers. The first option consists solely of whole numbers, which are rational as they can be represented as fractions (e.g., 1 can be expressed as 1/1). The third option includes a decimal (2.5) that can also be expressed as a fraction (5/2), making it rational. Lastly, all integers are defined as rational since they can be represented as a fraction with a denominator of 1.

Therefore, the choice that correctly identifies a set of numbers classified as irrational is the one that includes Pi and non-terminating decimals.