What is the Meaning of Mathematical Operator That There is a Bulge in the Lower Part of The Absolute Operator

Question

I am trying to figure out a question from the mathematical olympiads in 1998-1999.

What is the mathematical operator inside the red rectangle? Thanks in advance.

Answer 1

This denotes the floor function; there is also a related ceiling function.

• $\newcommand{\floor}[1]{\left \lfloor #1 \right \rfloor} \newcommand{\ceil}[1]{\left \lceil #1 \right \rceil} \floor{x}$ (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.