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- How do the floor and ceiling functions work on negative numbers . . .
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 If gravity were reversed, the ceiling would become the floor So from a physics
- 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
- Proving that floor (n 2)=n 2 if n is an even integer and floor (n 2 . . .
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 =
- 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?
- 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
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