Question 47794
It is called "the greatest integer function" .

[2x]=is defined on distinct intervals of x
For example:
[2x]=0 for 0<=x<1/2 because the greatest integer in the values generated is 0.
[2x]=1 for 1/2<=x<1 because the greatest integer in the values generated is 1.
etc.
Cheers,
Stan H.