论文标题
（避免）矛盾的证明：$ \ sqrt {2} $不是理性的
(Avoiding) Proof by Contradiction: $\sqrt{2}$ is Not Rational
论文作者
论文摘要
我们提供了另一种证据，证明$ \ sqrt {2} $是不合理的，它不是从假设$ \ sqrt {2} $实际上是合理的。
We provide an alternative proof that $\sqrt{2}$ is irrational that does not begin with the assumption that $\sqrt{2}$ is in fact rational.
