floor function ⌊x⌋

Math symbols chosen for obvious reason.
Typically named "floor()" in text software.

"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.
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 (-1.0,-2.0] 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:    ⌊ ⌊     ⌋ ⌋