Algorithms-Meanings of mathematical terms and mathematical terms in discrete mathematics, and answers to discrete mathematics and Algorithms

Algorithms-Meanings of mathematical terms and mathematical terms in discrete mathematics, and answers to discrete mathematics and Algorithms

Here we will introduce two important functions in discrete mathematics: The base function and the top function. Make x a real number. The base function rounds x to an integer smaller than or equal to x and closest to x, while the top function rounds x to an integer greater than or equal to x and closest to x. These two functions are often used to count the number of objects. These two functions play an important role in analyzing the number of steps used in computer processes to solve problems of a certain scale.

Definition:The maximum integer that the base function assigns to the real number x is smaller than or equal to x. The base function value in x is represented by limit x limit. The top function assigns a minimum integer greater than or equal to x to the real number x. The value of the top function in x is represented by limit x limit.

Note:The base function is also known as the maximum integer function, which is usually represented by [x.

For example, the following are the values of the base function and the top function.

Average 1/2 bytes = 0, average 1/2 bytes = 1, average-1/2 bytes =-1, average-1/2 bytes = 0,

Listen 3.1 records = 3, listen 3.1 records = 4, listen 7 records = 7, then 7 records = 7

Nature:

Limit x Limit = n when and only when n <= x <n + 1, where n is an integer

Limit x Limit = n when and only when n-1 <x <= n, where n is an integer

Limit x Limit = n when and only when the X-1 <n <= x, where n is an integer

Limit x Limit = n when and only when x <= n <x + 1, where n is an integer