高斯函数[x]是一个特殊的函数,在数学竞赛中经常出现,在近几年高考试题中也偶尔出现.本文介绍高斯函数的定义、基本性质和典型问题,供读者参考.设x∈R,用[x]表示不超过x的最大整数,则y=[x]称为高斯函数(这一函数最早由高斯引入,故得名),也叫取整函数.任意实数x都能写成整数部分与非负纯小数部分之和x=[x]+r(0≤r<1),这里[x]为x的整数部分,r=x-[x]为 Gaussian function [x] is a special function that often appears in math competitions, and also appears occasionally in the entrance exam questions in recent years.This paper introduces the definition, basic properties and typical problems of Gaussian function, for readers' reference. Let x∈R , [X] is the largest integer not exceeding x, then y = [x] is called a Gaussian function (this function was originally introduced by Gauss, hence the name), also called the rounding function. Any real number x can be written as an integer X = [x] + r (0 ≦ r <1), where [x] is the integer part of x and r = x- [x] is the sum of the part and the nonnegative fractional part