Understanding the meaning of the notation $([x_{i-1},x_i],t_i)$

Question

When learning about tagged partitions I'm introduced to the notation $([x_{i-1},x_i],t_i)$. Is this referring to all numbers y such that $x_{i-1}<y<t_i$ ? Or does it mean something else? Cheers

Answer 1

If $P=\{x_0,x_1,...,x_n\}$ is a partition of the intervall $[a,b]$, then put $I_i:=[x_{i-1},x_i], \quad (i=1,...,n) $.

Then $([x_{i-1},x_i],t_i)$ means that $t_i \in I_i.$