1. If a set $S$ satisfies that for any $a, b \in S$, $a \pm b \in S$, then the set $S$ is called a "closed set". Among the following sets, which one is not a closed set? ( ).
(A) Set of natural numbers $\mathbf{N}$
(B) Set of integers $\mathbf{Z}$
(C) Set of rational numbers $\mathbf{Q}$
(D) Set of real numbers $\mathbf{R}$
-,1.A.
By the definition of a closed set, we know that the set of integers $\mathbb{Z}$, the set of rational numbers $\mathbb{Q}$, and the set of real numbers $\mathbb{R}$ are all closed sets, but the set of natural numbers $\mathbb{N}$ is not a closed set.