Which of the following represents a set of irrational numbers?

The set of irrational numbers is characterized by numbers that cannot be expressed as a simple fraction or ratio of two integers. They have non-repeating, non-terminating decimal expansions. The square root of 3 and pi are both examples of such numbers. The square root of 3 is an irrational number because it cannot be exactly represented as a fraction, and its decimal form goes on forever without repeating (approximately 1.732...). Similarly, pi (π) is also an irrational number, commonly approximated as 3.14159 but has a decimal expansion that continues infinitely without repeating.

In contrast, the other options are either rational numbers, which can be expressed as fractions, or they fall into categories that do not include irrational numbers. For instance, the first choice consists of two rational numbers (2/3 and 0.5), which can both be expressed as fractions. The other two options include integer values and whole numbers, both of which are also rational since they can be expressed simply as fractions (e.g., any integer n can be written as n/1). Therefore, the only correct representation of a set that consists of irrational numbers is indeed the one containing the square root of 3 and pi.