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.

The floor function turns continuous integration problems in to discrete problems, meaning that while you are still "looking for the area under a curve" all of the curves become rectangles.

] {floor(3*x)+2}; \end{axis} \end{tikzpicture} \end{document} The sample points are marked. The number of samples is the number of lines plus one for an additional end point: It works only, because x …

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...

What do you mean by “a more mathematical approach (rather than using a defined floor/ceil function)”? I don't see how having predefined modulo is more mathematical than having predefined floor or …

When floor a number, you can think of it as replacing the Mantissa with $0$ $$\lfloor 2.31 \rfloor = 2 + 0 = 2$$ and ceil can be thought of as replacing the mantissa with $1$. $$\lceil 2.31 \rceil = 2 + 1 = 3$$ …

It looks to me as though TiKZ is sampling at data points which are unevenly spaced from grid cell to grid cell. I suspect that the plot is perfectly correct, except that the points on the x-axis which it is …

18 There are some threads here, in which it is explained how to use \lceil \rceil \lfloor \rfloor. But generally, in math, there is a sign that looks like a combination of ceil and floor, which means round, …

If you try asking Wolfram Alpha to differentiate the floor function, it will just output "Floor' (x)". If you force Wolfram Alpha to plot the derivative of the floor function, I think what Wolfram Alpha does is it as an …

4 I suspect that this question can be better articulated as: how can we compute the floor of a given number using real number field operations, rather than by exploiting the printed notation, which …