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.
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