[Math] the mathematical notation for rounding a given number to the nearest integer

Question

What is the mathematical notation for rounding a given number to the nearest integer? So like a mix between the floor and the ceiling function.

Answer 1

I have seen $\lfloor x \rceil$. It must have been in the context of math olympiads, so I can't point to a book that uses it. Wikipedia suggest this notation, among others: nearest integer function.

Personally, I would prefer $[x]$, being a cleaner mix of $\lfloor x \rfloor$ and $\lceil x \rceil$. But I've seen this notation being used for the floor function. Especially in older texts, say, pre-TeX era.

You could also do something like $\mathrm{nint}(x)$, but in formulas that could be cumbersome.

See also the remarks at Mathworld.