The greatest integer function is defined as the greatest integer less than or equal to x.
for example,
[x] = greatest integer less than or equal to x.
[3.5] = 3
[-3.6] = -4 (because -4 is less than -3.6)
[-5]=-5
[12]=12
[ π ] = 3
[ π /2 ] = [ 1.57 ] = 1
[ π ] /2 = 3/2 = 1.5
[[ π ] /2 ] = [ 1.5 ] = 1
etc.
It is also called the floor function.