Greatest integer function

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This article is about a particular function from a subset of the real numbers to the real numbers. Information about the function, including its domain, range, and key data relating to graphing, differentiation, and integration, is presented in the article.
View a complete list of particular functions on this wiki


The greatest integer function is a function from the set of real numbers to itself that is defined as follows: it sends any real number to the largest integer that is less than or equal to it.

The greatest integer function of x is sometimes denoted [x]. However, the square brace notation [] is also used in a number of other contexts and should not always be construed as meaning the greatest integer function.

The greatest integer function is related to the fractional part function (sometimes denoted \{ \}) as follows: for any x \in \R, we have:

\! x = [x] + \{ x \}