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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?

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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.

http://mathworld.wolfram.com/NearestIntegerFunction.html

Edit: After closer inspection & looking at Hastad papers from 1988, I can't find the specific notation. I may be overlooking something or Mathworld could be wrong. If anyone could shed some light on the situation, I'd be greatful!

Papers: http://www.nada.kth.se/~johanh/papers.html , http://www.nada.kth.se/~johanh/fhkls.pdf , http://www.nada.kth.se/~johanh/latticeduallower.pdf

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  • $\begingroup$ Thank you. Strangely enough I didn't think of looking it up on Mathworld. $\endgroup$ – DavidButlerUofA Jul 27 '14 at 2:18
  • $\begingroup$ @DavidButlerUofA No problem but I'm not entirely sure that it's correct. $\endgroup$ – Jam Jul 27 '14 at 2:21
  • $\begingroup$ 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. $\endgroup$ – DavidButlerUofA Jul 27 '14 at 2:30
  • $\begingroup$ @DavidButlerUofA Good find; thanks. $\endgroup$ – Jam Jul 27 '14 at 2:30

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