Sep 12, 2019 · $\begingroup$ @richard1941 - You appear to have completely missed the point of my remark, which was to give an example of why "rounding to the nearest integer" is …

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⌋ ≤ …

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 …

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 …

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. …

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 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 …

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 …

floor returns the nearest lowest integer and ceil returns the nearest highest integer. All real numbers are made of a characteristic (an integer part) and mantissa (a fractional part) …

I like the combined floor/ceiling symbol for nearest integer, although Wolfram calls it "cumbersome" and "not recommended". When I was at school, if you wanted to show an …