取整运算中[x]和{x}

• 作 者: 王怀祥
• 机 构: 重庆江津贾嗣镇中学 402281
• 出 处: 数学教学通讯
• 发表日期: 2002年S2期
• 关键词: 整数部分 解不等式 高斯函数 数学教学 数学解题 数学竞赛 解题思路 化归 求值 正整数解

对于任意实数x,[x]表示不超过。的最大整数,符号[ ]叫做取整号,或叫高斯记号.取整运算(函数)又叫做高斯函数.由定义可知,[x]≤x,x=2.3时,[2,3]=2,x=-2.3时,[-2.3]=-3.与[x]密切相关的是x的小数部分,我们用{x}表示,在定义下,x减去它的小数部分就等于它的整数部分,即x-{x}=[x],因此x=

For any real number x, [x] means no more than. The largest integer, the symbol [] is called the rounding number, or Gaussian notation. The rounding operation (function) is also called the Gaussian function. By the definition, [x] ≤ x, x = 2.3, [2,3] = 2 When x=-2.3, [-2.3]=-3. Closely related to [x] is the fractional part of x. We use {x} to denote that, under the definition, x minus its fractional part is equal to its The integer part, x-{x}=[x], so x=