To understand a notation on Riemann integral

Question

I was reading proof of Riemann condition theorem on $\mathbb{R^n}$ that in the proof, I couldn't understand this:

''Choose a partition $P$ so that $L(f,P)$ is within $\epsilon/2$ of the integral $\int_Q f$ and a partition $P'$ so that $U(f,P')$ is within $\epsilon/2$ of the integral $\int_Q f.$''

My question is: Can you say that what is ''$L(f,P)$ is within $\epsilon/2$ of the integral $\int_Q f$'' mean as mathematically? Can you explain? I couldn't understand this sentence, especially ''within''. Thanks...

Answer 1

It means that $\int_Qf-L(f,P)<\frac\varepsilon2$.