直接证据是 方法 证明是指通过直接结合既定事实（通常是公理、定义和已证明的定理）来证明给定命题的真值。要证明条件命题 p → q，首先假设 p 为真，然后运用推理规则证明 q 也必然为真。
直接证明（数学）
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A direct proof is the most straightforward form of proof in mathematics. It proceeds logically from a set of premises or hypotheses to a conclusion. The structure typically follows a linear chain of reasoning. For instance, to prove the statement “If n is an odd integer, then n² is an odd integer,” a direct proof would start by assuming n is odd. By definition, an odd integer can be written as [latex]n = 2k + 1[/latex] for some integer k. Squaring this expression gives [latex]n^2 = (2k + 1)^2 = 4k^2 + 4k + 1[/latex]. This can be rewritten as [latex]n^2 = 2(2k^2 + 2k) + 1[/latex]. Since [latex]2k^2 + 2k[/latex] is an integer, let’s call it m, we have [latex]n^2 = 2m + 1[/latex]. By definition, this shows that n² is an odd integer. This example illustrates the core principle: using definitions and algebraic manipulation to directly arrive at the desired conclusion from the initial assumption. This method is fundamental and forms the basis of many more complex proofs. It relies on the law of detachment (modus ponens) in logic.
UNESCO Nomenclature: 1201
逻辑
类型
抽象系统
中断
基础
用法
广泛使用
前体
- 亚里士多德逻辑与三段论
- 古希腊公理系统的发展
- 欧几里得《几何原本》作为演绎推理的模型
应用程序
- 数学的基础
- 用于计算机科学中的算法正确性证明
- 在逻辑学和哲学中，运用这些方法构建有效的论证。
专利：
NA
潜在创新理念
相关概念：直接证明、逻辑、蕴涵、肯定前件式、公理、定理、演绎、条件语句、数学、推理。
历史背景
直接证明（数学）
（如果日期未知或不相关，例如“流体力学”，则提供其显著出现的近似估计）
