What are these symbols called?

Question

Discrete Mathematics and Its Applications, Kenneth H. Rosen, p. 244.

What do these symbols that look similar to square brackets ([]) mean? What are they called? I've seen these used throughout the book, but don't know precisely what they mean.

Answer 1

Books usually define the notations before they use them, and this one is no different.

Answer 2

I don't know what these are called, but they denote the floor and ceiling functions.

• $\newcommand{\floor}[1]{\left \lfloor #1 \right \rfloor} \newcommand{\ceil}[1]{\left \lceil #1 \right \rceil} \floor{x}$ (the floor function) returns the greatest integer less than or equal to $x$
• $\ceil{x}$ (the ceiling function) returns the least integer greater than or equal to $x$.

Loosely, they are like "round down" and "round up" functions, respectively.

For instance,

• $\floor{1.4} = 1$
• $\floor{2.9} = 2$
• $\floor{-1.5} = -2$
• $\floor{-2.9} = -3$
• $\ceil{1.4} = 2$
• $\ceil{2.9} = 3$
• $\ceil{-1.5} = -1$
• $\ceil{-2.9} = -2$

More info is on Wikipedia.