The Borel Sets of ℝⁿ Form a σ-Algebra, and Intervals of ℝ Are Sets

In the setting of Measure Spaces, Borel Sets and Lebesgue Measure on the Real Line: Standing Notation, let $n\in\mathbb{N}$.

(i) $\mathcal{B}(\mathbb{R}^{n})$ is a $\sigma$-algebra on $\mathbb{R}^{n}$, so $(\mathbb{R}^{n},\mathcal{B}(\mathbb{R}^{n}))$ is a measurable space.

Let $I$ be an interval of $\mathbb{R}$.

(ii) $I$ is a set.