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.

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 …

How would one go about proving the following. Any ideas as to where to start? For any integer n, the floor of n/2 equals n/2 if n is even and (n-1)/2 if n is odd. Summarize: [n/2] = n/2 if n = ...

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 …

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 = …

It natively accepts fractions such as 1000/333 as input, and scientific notation such as 1.234e2; if you need even more general input involving infix operations, there is the floor function …

For the floor function alone, you can refer to this question and its accepted answer. I regard your question as a different question, namely, once you have proved the existence of the floor, …

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, …

6 In class, we briefly covered what "floor" and "ceiling" mean. Very simple concepts. They were on one slide, and then we never heard about them again. But now the following homework …