2017年8月18日 · $\begingroup$ 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 floor it would first need to figure out where the decimal place is, and then replaces the corresponding digits (if any) to 0, and if the result would be 0, then the format switches to …

2013年6月8日 · \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 when a different size is required.

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. Floor always rounding towards zero. Ceiling always rounding away from zero. E.g floor(x)=-floor(-x) if x<0, floor(x) otherwise

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 need to add to find the value of the integral (being careful to understand that rectangles below the x-axis have "negative areas").

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⌋ ≤ 2x < 3⌊x⌋+1) but I am sure it is simpler this way

2016年2月17日 · I do not know how rigorous or formal you need/want to be but it's straight forward that $[x]$ is the unique integer such that $[x] \le x < [x] + 1$[*]

2012年1月25日 · 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 $\\ceil{x}$ instead of $\\lce...

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 represents the integer part of the argument obtained by suppressing the fractional part.

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 electronically stored) notation for a rational number which approximates a real number is a mathematical object.

2017年1月17日 · 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 can pass an optional explicit sizing instruction -- \Big and \bigg in the example code below -- or you can use the "starred" version of the macro -- \floor* -- to autosize ...