换句话说，这些命题——就好像宗教信仰里面认为上帝创造了世界一样——必须有事实证据做为支撑，并且可以通过讨论和在现实世界中做实验的方式来加以证明。
In other words, they are claims - like the claim that God created the world - that are supported by evidence, that are proved by arguments and tested against our experience of the world.
高德的不完备定理的主要结论是，所有的逻辑体系都会存在无法证明或证伪的命题。因此，所有的逻辑体系都不“完备”。
The main conclusion of Gödel’s incompleteness theorems is that all logical systems will have statements that cannot be proven or disproven; therefore, all logical systems must be “incomplete.”
作为课后作业，我们需要证明以下命题：如果灯过去是关着的，并且现在它是开着的，请证明有人按了开关我真的试着证明它了。我花了许多小时，试图证明这个命题。
For our homework, we had to prove the converse: if the light was off, and it's on now, prove that you flipped it.
这表明了世界上不存在能够证明或证伪所有命题的终极数学体系。
This is thought to indicate that there is no grand mathematical system capable of proving or disproving all statements.
一旦证明猜想是伪命题，那将使人们对现代数学的许多部分产生质疑——当然也包括基于庞加莱猜想的一切。
Proving the conjecture false would have cast doubt on much of modern mathematics-and everything that depends on it.
比方说某人有一条引理用于证明论文的主命题。
For instance, suppose one has a serviceable lemma that suffices for the task of proving the main theorems of the paper at hand.
本文应用形式矩阵的计算技巧，得到李善兰恒等式的一个等价命题，进而给出李善兰恒等式的一个初等证明。
In this article we apply formal matrices technique to get a equivalent proposition of Li Shanian identity, and hence give an elementary proof for Li Shanlan identity.
第三章是对这一命题的证明。
In the third chapter, we give an verification to this proposition.
渐近鞅型序列具有很好的性质，本文给出实值渐近鞅的四个等价命题，并应用停时理论对它们予以证明。
Amarts have very good properties. This paper gave the four equivalent propositions of R-Value's amart and their proofs by utilizing the theory of stopping time.
上下文：欧几里得关于毕德哥拉斯定理的证明利用了前已证明的命题41。
Context: Euclid's proof of the Pythagorean theorem made use of the previous proven theorem known as Proposition 41.
数学归纳法是一种证明与正整数有关的命题的极为有效的科学方法。
Mathematical induction is a positive integer proved extremely relevant to the topic of effective scientific methods.
通过一个命题的证明，得出关于W。
本文给出一类线性代数命题的一种证明方法。
A proof of a kind of linear algebra propositions is given in this paper.
本文以命题形式讨论无棱二面角的平面角大小的几种解法并加以证明和举例。
In the form of propositions, this paper discusses several solution methods of the size of dihedral angles and proof and example are also offered.
通过对康德的认识论命题“先天综合判断”与孔子的认识论命题“生而知之”、“学而知之”的比较可证明这一观点。
By comparing the epistemological proposition of "Congenital Comprehensive Judgment" by Kant and that of "Born with Knowledge" and "Learn to Get Knowledge" by Confucius, this opinion can be proved.
数学命题的证明步骤是由已知条件逐步推演形成的系统。
The proving procedures of mathematical propositions construct the system deduced progressively from known conditions.
的概念在历史上的启示作为替代命题的启示一方面或一般性的启示其他没有证明是成功的。
The concept of revelation in history as an alternative to propositional revelation on the one hand or general revelation on the other did not prove successful.
对于竞赛图中必有有向哈密顿路这一命题，在分析已有证明的基础上，给出了一种新的证明。
On the basis of analysing existed proofs, provides a new proof about the proposition that every tournament has a directed Hamilton path.
给出了相干命题逻辑自然推理系统NR的自动证明算法。
This paper presented an automated reasoning algorithm for natural deduction system (NR) of relevance propositional logic.
就如我在证明关于三角形的任何命题时，人虽然假定我着眼于一个普遍的三角形观念；
Thus when I demonstrate any proposition concerning triangles it is to be supposed that I have in view the universal Idea of a triangle;
也引申出命题逻辑定理证明的一个可信性问题。
Furthermore, it presents a creditability problem about theorem proof in propositional logic.
本文从几个命题的证明来阐述微分不等式的应用。
This article by seeking to prove propositions, set forth the application of differential inequality.
上下文：在一个证明过程中每一个陈述句都要被符合逻辑地用定义，定理或公理或前边已证明的命题加以判定。
Context: Each statement in a proof is logically justified by a definition, postulate, or an earlier proposition that has already been proven.
利用齐次线性方程组解的理论讨论矩阵的秩，给出几个关于矩阵秩的著名不等式的证明，并证明了两个命题。
The article discusses rank of a matrix by the solution theorem of system of homogeneous linear equations, and proves several famous inequalities and two propositions on rank of a matrix.
我所走过的路，足以证明，天长地久是多么可笑的逆命题。
I walked the streets, enough to prove that, forever is how ridiculous the inverse proposition.
引入了可分命题和可分命题定理，利用该定理统一证明数学分析中的定理，极大简化了这些定理的证明过程。
This article is to introduce separable proposition and separable proposition theorem, then to prove theorems in real number field by using separable proposition in a union form.
引入了可分命题和可分命题定理，利用该定理统一证明数学分析中的定理，极大简化了这些定理的证明过程。
This article is to introduce separable proposition and separable proposition theorem, then to prove theorems in real number field by using separable proposition in a union form.
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