Let $[a, b] \subset \mathbb{R}$ be a D544: Closed real interval such that

(i)	\begin{equation} a < b \end{equation}

An D548: Ordered pair $P = ((x_0, x_1, \ldots, x_N), (x^*_1, \ldots, x^*_N))$ is a tagged partition of $[a, b]$ if and only if

(1)	\begin{equation} a = x_0 < x_1 < \cdots < x_N = b \end{equation}
(2)	\begin{equation} \forall \, n \in \{ 1, \ldots, N \} : x_{n - 1} \leq x^*_n \leq x_n \end{equation}

Let $[a, b] \subset \mathbb{R}$ be a D544: Closed real interval such that

(i)	\begin{equation} a < b \end{equation}

An D548: Ordered pair $P = ((x_0, x_1, \ldots, x_N), (x^*_1, \ldots, x^*_N))$ is a tagged partition of $[a, b]$ if and only if

(1)	\begin{equation} a = x_0 < x_1 < \cdots < x_N = b \end{equation}
(2)	\begin{equation} \forall \, n \in \{ 1, \ldots, N \} : x^*_n \in [x_{n - 1}, x_n] \end{equation}