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t_4]</math>, and implies <math>t_2 = t_3</math>.
===
A ''
<math>(t_1,z_1)(t_2,z_2) \cdots (t_n,z_n)</math> over an event set <math> Z </math> and a time interval <math>[t_l, t_u] \subset \mathbb{T} </math> is concatenation of [[Event Segment#Unit event segment|unit event segments]] <math>\epsilon_{[t_l,t_1]},(t_1,z_1), \epsilon_{[t_1,t_2]},(t_2,z_2),\ldots, (t_n,z_n),</math> and <math>\epsilon_{[t_n,t_u]}</math> where
<math>t_l\le t_1 \le t_2 \le \cdots \le t_{n-1} \le t_n \le t_u</math>.
Mathematically, a event trajectory is a mapping <math>\omega</math> a time period <math>[t_l,t_u] \subseteq \mathbb{T} </math> to an event set <math>Z</math>. So we can write it in a function form :
<math> \omega:[t_l,t_u] \rightarrow Z^* </math>
== Timed language ==
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