Oct 15, 2024 · Closed form solution of a sum involving the floor function Hot Network Questions What are the details regarding the cause of brake fluid contamination, and why can't an air …

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 …

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⌋ ≤ …

I need something that corresponds to floor() to use it in a macro (I don't mean the notation, I really mean the function that rounds downwards). Something like this: \\floor{34.75} produces 34 A...

Jun 10, 2020 · By definition of floor, $\lfloor xy\rfloor$ must be the greatest such integer. Thus, we have $$\lfloor xy\rfloor \ge \lfloor x\rfloor\lfloor y\rfloor,$$ giving us the left inequality.

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 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. …

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 …

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 …

Jun 4, 2018 · So your formula is not well-defined unless you specify which branch you are considering to be the principal branch. The most natural way to specify the usual principal …