Again considering your first example, for $1 \leq x < 2$, the floor function maps everything to 1, so you end up with a rectangle of width 1 and height 1. It is the areas of these rectangles you …

Aug 18, 2017 · $\begingroup$ I think "simply" isn't quite the right word, maybe "effectively." IEEE 754 format (in normal form) stores numbers as $\pm 1.bbb...bb \times 2^n$, so to compute the …

so clearly the floor of x divided by x must be less then or equal to 2/3; or x divided by the floor of x is greater then or equal to 3/2; Of course there is another constraint that I have left out (3⌊x⌋ ≤ …

Jun 8, 2013 · \floor is not defined in amsmath. The \DeclaredPairedDelimiter' is good, but in comparison to the \newcommand` above it mostly provides an easy way to change the code …

The correct answer is it depends how you define floor and ceil. You could define as shown here the more common way with always rounding downward or upward on the number line. OR. …

When a computer evaluates floor(x), it's all math. The printed (or electronically stored) notation for a rational number which approximates a real number is a mathematical object. The printed (or …

Jan 25, 2012 · Is there a convenient way to typeset the floor or ceiling of a number, without needing to separately code the left and right parts? For example, is there some way to do …

The floor function (also known as the entier function) is defined as having its value the largest integer which does not exceed its argument. When applied to any positive argument it …

Jan 17, 2017 · A LaTeX-y way to handle this issue would be to define a macro called, say, \floor, using the \DeclarePairedDelimiter device of the mathtools package. With such a setup, you …

For floor rounding we eliminate the decimal part by subtracting the decimal part of the divided number from the divided results. For ceiling rounding we figure out the number that, when …