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The set of irrational numbers is formed by all numbers that cannot be expressed as the ratio between two integers. $\begin{gathered} \sqrt{3}, \quad \sqrt{5}, \quad \pi, \quad e \end{gathered}$ These example numbers are all real, but none can be expressed rationally.
Although this set doesn't have its own representative symbol, it is sometimes written as an expression involving other number set symbols. $\begin{gathered} \mathbb{R}-\mathbb{Q}\quad\text{or}\quad\mathbb{R}\ \setminus\ \mathbb{Q} \end{gathered}$