Final answer:
To show that the set {11, 14, 17, 20, 23, 26,…} is countable, we can define a function such as f(n) = 3n + 8 that maps each natural number to a unique term in the set, demonstrating a one-to-one correspondence.
Step-by-step explanation:
The student is given the set of numbers {11, 14, 17, 20, 23, 26,…}, which appears to be an arithmetic sequence. To establish that this set is countable, we can define a function that relates each element of this set to a unique natural number (positive integer). In other words, for each element in the set, there is exactly one natural number corresponding to it, showing a one-to-one correspondence between the elements of the set and the natural numbers.
An example of such a function would be f(n) = 3n + 8, where n is a natural number. The function value corresponds to each term in the given set. For example, f(1) = 11, f(2) = 14, and so on. This function shows that for each natural number, there is a distinct term in the set, hence proving the set is countable.