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.
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.
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.
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.
与此同时，实现了一些数学(群论)定理的机器证明，命题的逻辑推演等。
At the same time implemented machine proof of some mathematical theorems (Group theory) and logical Inference of statements.
如果能证明该蕴涵式为重言式，那么其数学命题的证明推理形式就是正确的。
If the containing type can be proved to be heavy speech type, the method of the mathematical proposition proving and reasoning is correct.
如果能证明该蕴涵式为重言式，那么其数学命题的证明推理形式就是正确的。
If the containing type can be proved to be heavy speech type, the method of the mathematical proposition proving and reasoning is correct.
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