I'm trying to work my way through a white paper on room pricing for hotel rooms. I'm working on upgrading my math knowledge with MOOCs, but I'm running into problems that haven't been covered yet, and I'm not sure where to look.
For example, the following incorporates some set-builder notation, I believe. If anyone could help me by either explaining what I'm not understanding or by pointing me in the right direction for topics to study, that would be awesome.
"To formulate this model, we define a stay in the hotel by (a,L,k), where ‘a’ is the first night of the stay, ‘L’ is the length of the stay and ‘k’ the price class. Further, denote the set of stays that make use of night ‘l’ by $N_l$, where $N_l = \{(a,L,k): l = a: a + L - 1\}$."
I haven't seen the colon (:) used before, only pipe (|). But another MathExchange post says that the colon (:) also means "such that."
So, this is basically saying to include stay $(a,L,k)$ such that the first night (a) equals the specified night, (l), such that the first night (a) plus the length-of-stay (L) minus 1. If that interpretation is correct, I still don't understand the third component. The second component could be evaluated as either true or false, but how is the third component evaluated? There's no comparison operator.
As this is my first post, I hope I've formatted everything correctly.
Thank-you AF