Final answer:
The set x is a real number is an infinite set because it consists of all possible real numbers on the continuous number line, which has no end and contains an uncountable number of elements.
Step-by-step explanation:
The set described as x consists of all possible real numbers. This is an infinite set because real numbers include all the numbers on the continuous number line, and there is no end to the numbers on this line. Since there are an uncountable number of elements between any two real numbers, the set cannot be finite.
The correct answer is: OD. The set is infinite because the elements of the set are not listed between the braces, separated by commas. However, a more precise reason the set is infinite is that real numbers form a continuum, and there is an infinite number of real numbers between any two distinct real numbers. Hence, the option OC could also be considered correct if it referred to the real nature of the numbers rather than their count being a whole number or not. In regular set notation, whether the elements are listed or not does not determine if a set is finite or infinite.