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The correct answer is it depends how you define floor and ceil When applied to any positive argument it represents the integer part of the argument obtained by suppressing the fractional part. 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 The floor function (also known as the entier function) is defined as having its value the largest integer which does not exceed its argument Ceiling always rounding away from zero

Is there a macro in latex to write ceil(x) and floor(x) in short form

The long form \\left \\lceil{x}\\right \\rceil is a bit lengthy to type every time it is used. What are some real life application of ceiling and floor functions Googling this shows some trivial applications. The pgfmath package includes a ceil and a floor function

The pgfplots offers a few options for constant plots (see manual v1.8, subsection 4.4.3, pp The option jump mark left for example might help. 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.

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 provided by package xintexpr. The height of the floor symbol is inconsistent, it is smaller when the fraction contains a lowercase letter in the numerator and larger when the fraction contains numbers or uppercase letters in the numerator Why is that the case How can i produce floor symbols that are always the larger size shown in the picture?

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.

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