Final answer:
The set {2,3,4,..., 13} is finite because it contains a specific number of elements which can be counted, specifically twelve integers.
Step-by-step explanation:
The set given in the question is {2,3,4,..., 13}. To determine whether this set is finite or infinite, we consider the number of elements within it. We see that it starts at 2 and ends at 13, which means it has a specific beginning and an end. Thus, this set is a collection of exact numbers and we can count the number of elements present, which are twelve integers. Hence, we conclude that this set is a finite set.
Examples of Finite and Infinite Sets
An example of a finite set could be the set of integers between 1 and 10, inclusive: S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. An infinite set, on the other hand, is one that goes on forever without an end, such as the set of all positive integers: A = {1, 2, 3, 4, ...}.