人工智能教程 - 数学基础课程1.5 - 离散数学-1

证明(proof)

是一种确定事实的方法

(A proof is a method for ascertaining the truth)

物理上和平时：

• 实验和观察(Experimentation & oberservation)
• 抽样和找反例(Sampling & counterexamples)
• 裁判(judge & jury)
• word of God
• Boss
• 内心的信念(inner conviction)
  例如在计算机科学里很流行的一句话:“信不信由你，我的程序里没有bug！”
  (It is very popular in computer science.believe it or not,with the mantra.there are no bugs in my program)

数学证明

是通过一系列公理的逻辑推理来验证一个命题

(A methematical proof is a verigication of a proposition by a chain of logical deductions from a set of axioms)

命题是真或假的陈述：
(A proposition is a statement that is either true or false)

Ex:$\forall n \in \mathbb{N} n^2+n+41$ is a prime number

$\forall$ for all 【量词】(quantifier)
$\mathbb{N}$ {0,1,2,3,…}【论域】(universe of discourse)
$n^2+n+41$ is a prime number :谓词(predicate)

谓词是一个命题，它的真值依赖于变量的值
(a predicate is a propostion whose truth depends on the value of a variable )

在实际的物理学和统计学中，你经常会通过检验前40个值
但即便前40个都正确，可能41就会是命题为假。

来源：CSDN

作者：KuFun人工智能

链接：https://blog.csdn.net/fsdaewrq/article/details/104276636