1. The problem is to understand the set notation $A = \{x \in \mathbb{N} : -2 \leq x\}$ and determine what elements belong to this set. 2. Here, $\mathbb{N}$ represents the set of natural numbers, which typically includes $\{1, 2, 3, \ldots\}$. 3. The condition $-2 \leq x$ means we are looking for natural numbers $x$ that are greater than or equal to $-2$. 4. Since all natural numbers are positive and greater than or equal to 1, the condition $-2 \leq x$ is always true for any $x \in \mathbb{N}$. 5. Therefore, the set $A$ includes all natural numbers: $A = \{1, 2, 3, \ldots\}$. 6. In summary, $A = \mathbb{N}$ because the inequality $-2 \leq x$ does not restrict the natural numbers.