Meaning of floor in equations

By reading the title it may sound like a silly question, but I have a data structures exam tomorrow and some formulas I need to know for algorithm analysis are read as (n – floor(log (n + 1)). What is the meaning of floor?

Thanks

Solution

floor(x) is the largest integer not greater than x. You can easily find this information on the web, here for example.

e.g.

floor(1.12) = 1  
floor(0.53) = 0
floor(-3.4) = -4

One thing that can confuse people is the floor of a negative value. Some might initially think that floor(-3.4) is -3 when in reality it is -4 by the definition of floor(x).

As a note, floor(x) is often written as enter image description here .