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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 [n/2] = n/2 if n =. For example, is there some way to do $\\ceil{x}$ instead of $\\lce.

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Is there a macro in latex to write ceil(x) and floor(x) in short form Any ideas as to where to start The long form \\left \\lceil{x}\\right \\rceil is a bit lengthy to type every time it is used.

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. Solving equations involving the floor function ask question asked 12 years, 6 months ago modified 1 year, 9 months ago 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 represents the integer part of the argument obtained by suppressing the fractional part.

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. 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?

What are some real life application of ceiling and floor functions Googling this shows some trivial applications. How would one go about proving the following