Greatest integer function

This function rounds any number down to the nearest integer. Let's use the notation GIF[x]for this site to mean greatest integer function of x. Another name for it is the floor function. So here are some examples: GIF[.9]=0 GIF[1.9]=1 Gif[-1.8]=-2 Here is one trick GIF[1.99999 where 9 repeats forever]=2 (I can not put the bar over it, but usually it would be written as 1.9 with a bar over the 9) The reason is that 1.999999999 forever is =2 so GIF[2]=2