# Notation for rounding function

The Wikipedia article http://en.wikipedia.org/wiki/Nearest_integer_function mentions the following notation for the rounding or "nearest integer" function. (That is, the function that corresponds to the ordninary rounding where you go up if the fractional part is more than half, and down if less than half.)

$$\lfloor x \rceil$$

This notation appeals to me because it is similar to the notation of $\lfloor x \rfloor$ for floor and $\lceil x \rceil$ for ceiling.

How common is this notation for rounding, and is there a reference for its first use?

Wolfram Mathworld gives it as from Hastad et al. 1988 though I haven't seen it before. It seems like sensible notation due to the possible confusion of $[x]$ with square brackets.
• Here is the paper that Mathworld references: epubs.siam.org/doi/abs/10.1137/0218059. The notation is mentioned for the first time on the second page, though there they use $\lceil x \rfloor$. Feel free to edit this into your answer. – DavidButlerUofA Jul 27 '14 at 2:30