"Round down" function. But note what that means for the negatives.
For positive numbers floor is same as truncate but for negative numbers it's not.
Domain is R. Range is Z.
Example: all x in half-open interval [1.0,2.0) i.e. includes 1 but not 2,
map to 1:
floor(1)=1
floor(1.23456)=1
floor(1.99999999)=1
Example: all x in half-open interval [-2.0,-1.0), i.e. includes -2 but not -1,
map to -2:
floor(-1.0000001)=-2
floor(-1.99999999)=-2
floor(-2)=-2
Also can be described as "nearest integer not greater than" function.
Made more use of in computer science than in math.
An example of a step function.
Periodic "jump" discontinuities.
Limit not defined at each integer because left and rght limits differ.
Otherwise, lim(x->c) f(x) = ⌊x⌋
HTML symbols: ⌊ ⌊ ⌋ ⌋