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Is there a macro in latex to write ceil(x) and floor(x) in short form Is there a way to draw this sign in latex's math mode? The long form \\left \\lceil{x}\\right \\rceil is a bit lengthy to type every time it is used.

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The correct answer is it depends how you define floor and ceil But generally, in math, there is a sign that looks like a combination of ceil and floor, which means round, aka nearest integer You could define as shown here the more common way with always rounding downward or upward on the number line.

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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. I understand what a floor function does, and got a few explanations here, but none of them had a explanation, which is what i'm after Can someone explain to me what is going on behind the scenes. \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 values for the sample points except the first are a tiny bit (rounding error) too small A more stable solution is to use the middle points of the. What are some real life application of ceiling and floor functions

Googling this shows some trivial applications.

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? The most natural way to specify the usual principal branch of the arctangent function basically uses the idea of the floor function anyway, so your formula for the floor function is correct but somewhat circular.

18 there are some threads here, in which it is explained how to use \lceil \rceil \lfloor \rfloor