Let $x$ in $[0,\frac{\pi}2]$ such that...

Question

In the following quote,

"Let $x$ in $[0,\frac{\pi}2]$ such that..."

what does this mean?

Answer 1

This means $x$ is some real number that is at least $0$ and at most $\tfrac{\pi} {2}$. If $a$ and $b$ are real numbers and $a < b$, the notation $[a,b]$ denotes the interval on the real line from $a$ to $b$, i.e. the set of real numbers which are between $a$ and $b$, including $a$ and $b$.