1. The question seems to be about the meaning of the symbols \(\mathbb{N}\), \(\mathbb{Z}\), \(\mathbb{Q}\), and \(\mathbb{R}\). 2. These are standard notations for different sets of numbers in mathematics: - \(\mathbb{N}\) represents the set of natural numbers, typically \(\{1,2,3,\ldots\}\) or sometimes \(\{0,1,2,3,\ldots\}\). - \(\mathbb{Z}\) represents the set of all integers, i.e., \(\{\ldots,-2,-1,0,1,2,\ldots\}\). - \(\mathbb{Q}\) represents the set of all rational numbers, which can be expressed as a fraction \(\frac{p}{q}\) where \(p, q \in \mathbb{Z}\) and \(q \neq 0\). - \(\mathbb{R}\) represents the set of all real numbers, which includes all rational and irrational numbers. 3. These sets are ordered by inclusion as: $$\mathbb{N} \subseteq \mathbb{Z} \subseteq \mathbb{Q} \subseteq \mathbb{R}$$ 4. Thus, these symbols denote common important sets of numbers used in algebra and analysis.