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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 ... 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 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. 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...

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.

A LaTeX-y way to handle this issue would be to define a macro called, say, \floor, using the \DeclarePairedDelimiter device of the mathtools package. With such a setup, you can pass an optional explicit sizing instruction -- \Big and \bigg in the example code below -- or you can use the "starred" version of the macro -- \floor* -- to autosize the left and right hand brackets. Both ...

Solving equations involving the floor function Ask Question Asked 13 years, 2 months ago Modified 2 years, 5 months ago Some time ago I encountered this problem in a national IMO team selection test at some stage, and cannot find the solution myself nor find it anywhere else. We wish to find the number of integer

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.