Question

What is the set of subsequential limits of the sequence of all positive rationals?

A. The set of positive integers.
B. The set of positive rationals.
C. The set of real numbers.
D. The set of natural numbers.

Answer 1

The sub sequential limits of the sequence of positive rationals is the set of real numbers.

Step-by-step explanation:

The set of sub sequential limits of the sequence of all positive rationals is the set of real numbers (option C).

A sub sequential limit is a number that can be approached by a subsequence of a given sequence. In this case, the sequence of all positive rationals contains infinitely many numbers between any two numbers, which means its sub sequences can converge to any real number. Hence, the set of sub sequential limits is the set of real numbers.

Examples of sub sequential limits in this case are 2.71828 (the number e), 3.14159 (pi), and all other irrational numbers.