How do you use floor ceil in math, e. g. how does it work exactly? 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 $1$ $$\lceil 2 31 \rceil = 2 + 1 = 3$$ That's not a very popular way of thinking about it but it was the way I thought about it when I first started using it in programming
Floor function plot with TikZ - TeX - LaTeX Stack Exchange 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 sampling at is much more coarse than you might like
How to represent the floor function using mathematical notation? 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 separates the real and fractional part, making nearby integers instantly identifiable How about as Fourier series?
Prove that $\\lfloor\\lfloor x 2 \\rfloor 2 \\rfloor = \\lfloor x 4 . . . 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 problem has popped up: $$\lfloor\lfloor x 2 \rfloor 2 \rfloor = \lfloor x 4 \rfloor$$