The group (Q, +) is the set of rational numbers under addition. In this group, we are interested in finding the total number of finite order elements.

Definition of Finite Order Elements
An element g in a group is said to have finite order if there exists a positive integer n such that g^n = e, where e is the identity element of the group.

Identity Element in (Q, +)
In the group (Q, +), the identity element is 0. For any rational number q, q + 0 = q and 0 + q = q.

Finite Order Elements in (Q, +)
Let's consider an arbitrary rational number q in (Q, +). In order for q to have finite order, there must exist a positive integer n such that q^n = 0.

Case 1: q = 0
If q = 0, then q^n = 0^n = 0 for any positive integer n. Therefore, 0 has finite order.

Case 2: q ≠ 0
If q ≠ 0, then q^n = 0 implies that q = 0. However, by assumption, q ≠ 0. Therefore, there are no nonzero rational numbers with finite order in the group (Q, +).

Total Number of Finite Order Elements
From the above analysis, we can conclude that the only rational number with finite order in the group (Q, +) is 0. Therefore, the total number of finite order elements in (Q, +) is 1.

Summary
- The group (Q, +) consists of rational numbers under addition.
- An element g in a group has finite order if there exists a positive integer n such that g^n = e, where e is the identity element of the group.
- In (Q, +), the identity element is 0.
- The only rational number with finite order in (Q, +) is 0.
- Therefore, the total number of finite order elements in (Q, +) is 1.