I'd like to point out that's the "Ceil function", or Ceiling so-called, [[x]], the way it works is, it defaults to the greatest integer, for example
[[ 3.5 ]] = 4
[[ 4.0001 ]] = 5
[[ - 3.5 ]] = -3 <--- recall on the negatives, the closer to 0, the larger.
so [[ x ]], or to be properly formatted ⌈x⌉ namely ceil(x), as opposed to ⌊x⌋ which means floor(x).
anyhow, ⌈x⌉ or [[x]] as many books use, results in the greatest integer, as you see the examples above.
[[ 4.0001 ]] results in 5, because between 4 ........ 4.0001......... 5, 5 is the larger of the extremes.
[[ -3.5 ]], betweeen -4 ........ -3.5.........-3, -3 is the larger, since is closer to 0.
