Imagine a vertical number line, and put x at a point in the middle. Then the next point above and below x are the “caps” for x, ceiling and floor (respectively).
^ ^ | | + ceil(x) + 6 | | + x . 5.7 | | + floor(x) + 5 | | v v
This makes more sense with real numbers (decimals), when x is desired to be an integer. For example, merge sort partitions the array and we need integers for the indices. You can’t get the 5.5th index of a number, although you might get that dividing an 11-element array.